tag:blogger.com,1999:blog-87375608384081498952024-03-20T01:44:17.735-07:00Behavioral Game TheorySome random thoughts on game theory, behavioural economics, and human behaviour Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.comBlogger119125tag:blogger.com,1999:blog-8737560838408149895.post-27485338987519112532019-05-12T00:57:00.001-07:002019-05-12T00:57:16.040-07:00Some estimates of cross-price elasticity<br />
The final part of this exciting trilogy is cross-price elasticity. (See here for estimates of <a href="https://econbeh.blogspot.com/2019/05/some-estimates-of-price-elasticity-of.html" target="_blank">own price</a> and <a href="https://econbeh.blogspot.com/2019/05/some-estimates-of-income-elasticity-of.html" target="_blank">income</a> elasticity.) Here we are looking for how demand for one product, say cars, is influenced by the price of another product, say petrol. The idea is to find a spread of examples from goods that are close substitutes (have cross price elasticity near 1) to strong complements (have an elasticity near -1).<br />
<br />
Within the literature there are a lot more examples of substitutes, like cars and public transport, than of complements, like cars and petrol. Indeed, it was a bit of a struggle to find any complements. Here are the examples I converged on:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNRtgCx_HhRa6OxV1vh-kSNhefQZ4LtxEm4rAjbUzD2u-mWx7WJzBVmUKNARVjTbFdFRDyV98tAVqun8_JP547jO_hQRh1fdFWAsN9Ox4aWGsRpMRBnkwLNcI5oHoNNj8IFCcUkKLKnsI/s1600/cross2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="142" data-original-width="293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNRtgCx_HhRa6OxV1vh-kSNhefQZ4LtxEm4rAjbUzD2u-mWx7WJzBVmUKNARVjTbFdFRDyV98tAVqun8_JP547jO_hQRh1fdFWAsN9Ox4aWGsRpMRBnkwLNcI5oHoNNj8IFCcUkKLKnsI/s1600/cross2.jpg" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
The <b>book</b> versus culture number is taken from the <a href="https://link.springer.com/article/10.1007/s10824-006-9006-7" target="_blank">study</a> by Ringstad and Loyland. The numbers for <b>organic food</b> are taken from the <a href="https://library.wur.nl/WebQuery/wurpubs/reports/351868" target="_blank">report</a> by Bunte and co-authors on Dutch data. Those for <b>alcohol</b> are from a UK a <a href="https://www.sciencedirect.com/science/article/pii/S0167629613001835" target="_blank">study</a> by Meng and co-authors.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPdguT1vgc8CcJoip1LtspOiUYIcMGOzKriEOx2pODvs_gjZpoFEoy_MPGZrS7F_LOmPD4a0NWu1A6xni8X6GNC6jjxRDDcMWs73720dPZs6EJ2_A4FXnmr7hmmiOCwphIxumcfyxEips/s1600/cross1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="221" data-original-width="710" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPdguT1vgc8CcJoip1LtspOiUYIcMGOzKriEOx2pODvs_gjZpoFEoy_MPGZrS7F_LOmPD4a0NWu1A6xni8X6GNC6jjxRDDcMWs73720dPZs6EJ2_A4FXnmr7hmmiOCwphIxumcfyxEips/s640/cross1.jpg" width="640" /></a></div>
<br />
<br />
For numbers of <b>public transport</b> in the UK there is a <a href="https://www.sciencedirect.com/science/article/abs/pii/S0967070X05001587" target="_blank">study</a> by Paulley and co-authors.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc4i126XmkR1BvSVi5ZABPvmVvddVP_q7lTdotgmVogcOKqmnaC-AbCDLDfXPZccrhyG8QzJjxoCg4LtNh2gnpgpBL5GJazeOL4mRFvFWb40XMOA9tB_PxtEj_2NIdS7u8vBFA7xm1_lo/s1600/price7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="167" data-original-width="712" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc4i126XmkR1BvSVi5ZABPvmVvddVP_q7lTdotgmVogcOKqmnaC-AbCDLDfXPZccrhyG8QzJjxoCg4LtNh2gnpgpBL5GJazeOL4mRFvFWb40XMOA9tB_PxtEj_2NIdS7u8vBFA7xm1_lo/s640/price7.jpg" width="640" /></a></div>
<br />
The <b>cocaine</b> number is taken from the <a href="https://www.sciencedirect.com/science/article/pii/S0376871600001575" target="_blank">study</a> by Petry. That brings us on to food. I was expecting to easily find numbers for food, and get some examples of complements. But my impression is that things have not really moved on much since the work of Angus Deaton in the 1980s. So, why not stick with those numbers, these taken from a <a href="http://www.princeton.edu/~deaton/downloads/Price_Elasticities_from_Survey_Data.pdf" target="_blank">study</a> using Indonesian data.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhX7FT4OeWYB9-V0FGWsAcXXlQaw6-9c12RGUGk2vhHapTcQwgF3i4JR182duVVRDawGWTLd_zQnvQCLuGvhGSusOYWGi4urJZVWS82A-pVERJAt_2wfvTN919O5YLMbhYsIb4Xqj73CbU/s1600/cross3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="497" data-original-width="645" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhX7FT4OeWYB9-V0FGWsAcXXlQaw6-9c12RGUGk2vhHapTcQwgF3i4JR182duVVRDawGWTLd_zQnvQCLuGvhGSusOYWGi4urJZVWS82A-pVERJAt_2wfvTN919O5YLMbhYsIb4Xqj73CbU/s640/cross3.jpg" width="640" /></a></div>
<br />
<br />
<br />Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-40331676911774735132019-05-11T23:14:00.001-07:002019-05-11T23:14:09.233-07:00Some estimates of income elasticity of demandMy <a href="https://econbeh.blogspot.com/2019/05/some-estimates-of-price-elasticity-of.html" target="_blank">previous blog</a> looked at estimates of own price elasticity of demand. Now the focus moves on to estimates of income elasticity of demand. In a sense income elasticity should be easier to measure than price elasticity of demand because there is more variation in income than price. But I actually found it a lot harder to come by income elasticicities in the literature.<br />
<br />
And it was particularly difficult to get a nice spread of elasticities. Ideally we want some examples of luxury goods (with elasticity more than 1), normal goods (more than 0) and inferior goods (less than 0). The large majority of the examples I could find fitted in the 0.3-0.8 range. My rough interpretation of the literature is that 'simple' estimates tended to suggest things like eating out and health care were highly income elastic but more detailed work has lowered the numbers down.<br />
<br />
It was also the case that goods you might think of as luxuries where not. This could just be a self-selection issue. For instance, organic food seems to be income inelastic for those that buy organic food. But, I'm guessing those that buy organic food are relatively well-off. Drug addiction seems another variant on this theme with a <a href="https://onlinelibrary.wiley.com/doi/abs/10.1046/j.1360-0443.2000.9557056.x" target="_blank">study</a> by Petry finding that demand is income elastic for addicts (and 0 for non-addicts). Which is illustrates the more general point that one person's luxury may not be another's meaning it is difficult to find goods that are luxuries 'on average'.<br />
<br />
Anyway, here are the numbers I settled on:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5bVeTypMPA3nEREOM1SA0tvUzRCYRyF2IjSgu7-NTPWaZ-yZM3Iehp8FVTFe0vx3MOdDu_KnAbxvV08fSCR2nBEhHm8KtThvv_3TGJP2LFCrbg-pbONVFT3N0_cwPkPtLo992BS7Eh9I/s1600/income5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="242" data-original-width="214" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5bVeTypMPA3nEREOM1SA0tvUzRCYRyF2IjSgu7-NTPWaZ-yZM3Iehp8FVTFe0vx3MOdDu_KnAbxvV08fSCR2nBEhHm8KtThvv_3TGJP2LFCrbg-pbONVFT3N0_cwPkPtLo992BS7Eh9I/s1600/income5.jpg" /></a></div>
<br />
<br />
My earlier post had an income elasticity of Israelis going on <b>vacation</b> of 0.28. Yet a study by <a href="https://www.tandfonline.com/doi/abs/10.1080/1350485042000338626" target="_blank">Maloney and Montes-Rojas</a> puts the elasticity for going to the Caribbean at 2.02. These are not necessarily inconsistent if we think of the Caribbean as a luxury destination. So, going on holiday is normal but going somewhere further afield is luxury.<br />
<br />
I have already mentioned the study by Petry where I got the cocaine number from. I will also mention a <a href="https://link.springer.com/article/10.1007/s00181-009-0302-x" target="_blank">study</a> by Celements and co authors that got an income elasticity of 1.3 for marijuana. Interestingly tobacco and alcohol come in a lot below 1 and so there is potentially an interesting story to be told there.<br />
<div>
<br /></div>
<div>
My search for luxury goods eventually paid off with a <a href="https://link.springer.com/article/10.1007/s10824-006-9006-7" target="_blank">study</a> of <b>books</b> by Ringstead and Loyland. They were using data from Norway before 2000 and so I'm not sure how representative that is of modern demand for books. But, it is easy to imagine that books are even more of a luxury good now that other sources of entertainment have a low marginal cost. </div>
<div>
<br /></div>
<div>
A study by Costa-Font and co-authors <a href="https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-985X.2010.00653.x" target="_blank">review</a> studies on <b>health care</b> and find an elasticity between 0.4 and 0.8. Crucially this means the health expenditure is not a luxury good - as many previously argued. A <a href="http://www.nkd-group.com/ghdash/mba555/PDF/Cross_Section_Housing_Spain.pdf" target="_blank">study</a> of <b>housing</b> in Spain by Fernandez-Kranz and Hon - with plenty of comments on the literature - came up with a number between 0.7 and 0.95.</div>
<div>
<br /></div>
<div>
Some numbers on <b>fuel consumption</b> are provided in a <a href="https://www.researchgate.net/profile/Joyce_Dargay/publication/32885803_Elasticities_of_Road_Traffic_and_Fuel_Consumption_with_Respect_to_Price_and_Income_A_Review/links/0deec5331bfbe7074c000000/Elasticities-of-Road-Traffic-and-Fuel-Consumption-with-Respect-to-Price-and-Income-A-Review.pdf" target="_blank">review</a> by Goodwin, Dargay and Hanly. For electricty use there is a German <a href="https://www.sciencedirect.com/science/article/pii/S0301421516307194" target="_blank">study</a> by Schulte and Heindl that gives detailed estimates:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRV8dnpW0vfgrvsckjJCj2FKYBb2NnVt8rDkUXMjAFhzYxnGXaZYftu9CpQwV7V7JhnsDzx8OgyDK7P0Tan5SLXs6nagicqIzcI9gWkgbLhQtTIgLIVDMXzmuom0j1kLTJ8wZaqKVw0ww/s1600/income4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="515" data-original-width="445" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRV8dnpW0vfgrvsckjJCj2FKYBb2NnVt8rDkUXMjAFhzYxnGXaZYftu9CpQwV7V7JhnsDzx8OgyDK7P0Tan5SLXs6nagicqIzcI9gWkgbLhQtTIgLIVDMXzmuom0j1kLTJ8wZaqKVw0ww/s640/income4.jpg" width="552" /></a></div>
</div>
<div>
<br /></div>
<div>
<br /></div>
<div>
We then get into <b>food</b>. For an interesting discussion on measuring food elasticites the <a href="https://royalsocietypublishing.org/doi/pdf/10.1098/rstb.2010.0164" target="_blank">review</a> by Cirera and Masset is recommended. But that does not give much by way of 'simple' numbers. For studies in Europe you can look at the references in my earlier post. A <a href="https://ageconsearch.umn.edu/record/109408/files/1-P-Kumar.pdf" target="_blank">study</a> by Kumar and co-authors gives some comparative numbers for India. You can see how income elasticity varies by income group meaning that Engel curves are definitely not straight lines. </div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin8w7S_PKj1CA9Tf6YXbyKdZQ1qqHWI3nPvMEDZHDvnfBi0uobe648sJYnSjifjS246FiGFofHe_BXtRyXVrXWnuaJz71Q0Rz4aSZzB9lrhI3KjdmSrCMpofx1iUisqq6xP3fysnhOmJk/s1600/income1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="467" data-original-width="1046" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin8w7S_PKj1CA9Tf6YXbyKdZQ1qqHWI3nPvMEDZHDvnfBi0uobe648sJYnSjifjS246FiGFofHe_BXtRyXVrXWnuaJz71Q0Rz4aSZzB9lrhI3KjdmSrCMpofx1iUisqq6xP3fysnhOmJk/s640/income1.jpg" width="640" /></a></div>
<br />
For food there is a lot more data out there. For instance a <a href="http://www.jsd-africa.com/Jsda/V12No2_Spring2010_B/PDF/Analysis%20of%20Demand%20For%20Rice%20in%20Ile%20Ife,%20Osun%20State,%20Nigeria.pdf" target="_blank">study</a> by Kassali and co-authors looks at rice demand in Nigeria and gets similar numbers to that in India. This can then be compared to numbers in Europe. So, here the numbers are a bit more definitive, but also fairly consistent in showing that most food items are in the range 0.2-0.7. Finally, the number I give for organic food is taken from a <a href="https://pubag.nal.usda.gov/pubag/downloadPDF.xhtml?id=22235&content=PDF" target="_blank">study</a> by Zhang and co-authors in the US. <br />
<br />
<br />
<br />
<br />Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-31745055922564754552019-05-06T01:13:00.001-07:002019-05-06T22:02:59.859-07:00Some estimates of price elasticity of demand<div style="text-align: justify;">
In the <a href="https://www.amazon.co.uk/Microeconomics-Behaviour-Robert-Frank/dp/0077174089/" target="_blank">textbook</a> on Microeconomics and Behaviour with Bob Frank we have some tables giving examples of price, income and cross-price elasticities of demand. Given that most of the references are from the 70's I'm working on an update for the forthcoming 3rd edition. So, here is a brief overview of where the numbers come from for the table on price elasticity of demand. Suggestions for other good sources much appreciated.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Before we get into the numbers - the disclaimer. Price elasticities are tricky things to tie down. Suppose you want the price elasticity of demand for cars. This elasticity is likely to be different for rich or poor people, people living in the city or the countryside, people in France or Germany etc.etc. You then have to think if you want the elasticity for buying a car or using a car (which includes petrol, insurance and so on). So, there is no such thing as <i>the</i> price elasticity of demand for cars. Moreover, the estimated price elasticity will depend on the actual price in the market and so there is a tricky endogeneity problem. And, that's feeds into the question of how to actually estimate elasticity from the data. Even so, it is interesting, particularly as an educational tool, to get a feel which goods are elastic and inelastic 'on average'.<br />
<br />
Here is the list I came up with, containing a range of goods from elastic to inelastic. Overall, though, most goods seemed to come out price inelastic. For more details on where these numbers come from see below.<br />
</div>
<div style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAoKiW5sbHF48Jybx1StVs51gZIwDNGllC6_PFujbsX-IYVlFHpovlvIaZrWgti9VMzos80bp_1HNr7I9H3dqd7x9g7xrRN-xJC1Dsgv65c7EQgNHwscMFljGM3q6sxqJZJphqh89DJDg/s1600/price+final.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="363" data-original-width="246" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAoKiW5sbHF48Jybx1StVs51gZIwDNGllC6_PFujbsX-IYVlFHpovlvIaZrWgti9VMzos80bp_1HNr7I9H3dqd7x9g7xrRN-xJC1Dsgv65c7EQgNHwscMFljGM3q6sxqJZJphqh89DJDg/s320/price+final.jpg" width="216" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br /></div>
<div style="text-align: justify;">
For <b>food</b> it is easy enough (at least for the US) to get some numbers thanks to a <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2804646/" target="_blank">study</a> by Andreyeva, Long and Brownell. They reviewed 160 studies to come up with the following numbers. As we might expect eating out is most price elastic. </div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkyHuBaU4yLvNEu_g0I_sjOGKjeday4Wt2YqFtvs28PXOmb0RCbWfyUPuXVVls3NNXmiSq7T-sYBMSzBRp2Sl9Hi9Gw5KZcpa1yoEC3N6b5L-JO5WJoTnIBtARJkOuqF7BeQJRrVV-tYs/s1600/price1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="511" data-original-width="404" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkyHuBaU4yLvNEu_g0I_sjOGKjeday4Wt2YqFtvs28PXOmb0RCbWfyUPuXVVls3NNXmiSq7T-sYBMSzBRp2Sl9Hi9Gw5KZcpa1yoEC3N6b5L-JO5WJoTnIBtARJkOuqF7BeQJRrVV-tYs/s400/price1.jpg" width="315" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Anything for the EU? A <a href="https://www-sciencedirect-com.proxy.library.dmu.ac.uk/science/article/pii/S0306919208000353" target="_blank">study</a> by Bouamra-Machemache and co-authors gives some evidence on <b>dairy </b>consumption. Fortunately, the numbers in this study match pretty well those from the US. But it is interesting to note the big range in estimates. For instance, cheese can have an elasticity of anything between 1.33 and 0.15; which seems pretty much like saying 'it could be anything'.</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5Lc8Phgycp6ugt-NAtchAEB59MFLas_wAc9tttcQ4SZIMe6h3LZltlAY6QU-GRv4TvDOkqILJgCOLYjn8KIi7BPgftzj_6FsZehWStEOTGIrpwaLIIfdUTQAr0io9HC73Y8_usXx_cZc/s1600/price2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="310" data-original-width="948" height="208" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5Lc8Phgycp6ugt-NAtchAEB59MFLas_wAc9tttcQ4SZIMe6h3LZltlAY6QU-GRv4TvDOkqILJgCOLYjn8KIi7BPgftzj_6FsZehWStEOTGIrpwaLIIfdUTQAr0io9HC73Y8_usXx_cZc/s640/price2.jpg" width="640" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
A nice <a href="https://library.wur.nl/WebQuery/wurpubs/reports/351868" target="_blank">report</a> by Bunte and co-authors looks in detail at organic food. First they give a review of the literature and then come up with some new estimates of their own for the Dutch market. We also have the comparison with non-organic good. Overall, we can see that organic food is a lot more price-elastic than non-organic food.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeWp2Kw6zwlXZmlVaBSG2nrvSPHRlp3_CKihbdzSLnBp_jJDkkrKvWVrBnYD_ZNtQquLebrhaOau1wIxwzud5vrnDVGD9cJ377AYcWtzlaaK_xEwyrAekQzO6k3PSHhcEopVSDOBfWKLI/s1600/price4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="413" data-original-width="1108" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeWp2Kw6zwlXZmlVaBSG2nrvSPHRlp3_CKihbdzSLnBp_jJDkkrKvWVrBnYD_ZNtQquLebrhaOau1wIxwzud5vrnDVGD9cJ377AYcWtzlaaK_xEwyrAekQzO6k3PSHhcEopVSDOBfWKLI/s640/price4.jpg" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMHyqDc1t-tnVwmDWY9xBH4Yq1zArZzg59eWx0jnG10oV3BmxStJW-8-EOH1oJGzr8ZYF03froFBj0vrRk1s56oLJvn9f9nGUXFtgYUscs9_TcbEqewH9Cd5YaWkQqcH-YN3o_dwzHi60/s1600/price5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="261" data-original-width="718" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMHyqDc1t-tnVwmDWY9xBH4Yq1zArZzg59eWx0jnG10oV3BmxStJW-8-EOH1oJGzr8ZYF03froFBj0vrRk1s56oLJvn9f9nGUXFtgYUscs9_TcbEqewH9Cd5YaWkQqcH-YN3o_dwzHi60/s640/price5.jpg" width="640" /></a></div>
<br />
Next to <b>alcohol</b> where there is a <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1360-0443.2008.02438.x" target="_blank">review</a> of 112 studies by Wagenaar, Salois and Komro. The figure below gives average elasticities from studies using aggregate level data. It is noticeable that demand seems relatively inelastic. </div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9iZtA-6wtwq7yDcu-Vw_TRu1stu0IzBpNaQgOJhpFMR4nIdeYLpmEEvkwOrEKRPfn4iSl0WcOmKQaY4iDcprLutnULucDlW_tUfaTRTNv8kJcXoclnEDiLOHHIdt-dDi4BCB8DIluno0/s1600/price3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="371" data-original-width="609" height="387" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9iZtA-6wtwq7yDcu-Vw_TRu1stu0IzBpNaQgOJhpFMR4nIdeYLpmEEvkwOrEKRPfn4iSl0WcOmKQaY4iDcprLutnULucDlW_tUfaTRTNv8kJcXoclnEDiLOHHIdt-dDi4BCB8DIluno0/s640/price3.jpg" width="640" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So far not a single good is price elastic. Which is not too surprising for food and drink. Let us, therefore, go to the other extreme and look at some entertainment goods. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
A <a href="https://pubsonline.informs.org/doi/abs/10.1287/mnsc.2014.1945" target="_blank">study</a> by Ghose and Han looked at demand for <b>mobile phone apps</b>. They find a price elasticity of demand of -3.731 for Google Play and -1.973 for the Apple App Store. So, firmly in the category of elastic demand. In terms of <b>broadband</b> a <a href="https://www.tandfonline.com/doi/abs/10.1080/000368497326462" target="_blank">study</a> by Madden and Simpson with Australian data finds a mean elasticity of -0.121. A <a href="https://www.sciencedirect.com/science/article/abs/pii/S0308596112001127" target="_blank">study</a> by Galperin and Ruzzier finds estimates of -0.36 for OECD countries compared to -2.2 for Latin American and Caribbean countries. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
For <b>football</b>, a <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9485.00235" target="_blank">study</a> by Forest, Simmons and Feehan gets an estimate of -0.74 in the Premier League. In terms of <b>cinema</b>, a <a href="https://www.sciencedirect.com/science/article/pii/S0167718714000174" target="_blank">study</a> by de Roos and McKenzie in Australia found an elasticity of around -2.5 while a <a href="https://link.springer.com/article/10.1007/s10824-005-6421-0" target="_blank">study</a> by Dewenter and Westermann in Germany found a similar number of -2.25. A <a href="https://link.springer.com/article/10.1007/s10824-012-9190-6" target="_blank">study</a> of Finnish <b>opera</b> by Laamanen got a figure of -0.69 for premieres and -3.99 for reprises. While a German <a href="https://link.springer.com/article/10.1007/s10824-009-9094-2" target="_blank">study</a> for <b>theatre</b> got a figure of -0.27. Even these entertainment goods seem relatively price inelastic.<br />
<br />
Finally, let us look at transport. A <a href="https://www.sciencedirect.com/science/article/abs/pii/S0967070X05001587" target="_blank">study</a> by Paulley and coauthors provides a comprehensive review of <b>public transport</b> with a UK focus. As we might expect demand is relatively inelastic. Note the interesting short-run versus long-run comparisons. For instance, bus journeys become elastic (just) in the long run.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFqa-pNOhYEheJSXrropkHos66CBxjYL3OJm-NVHpytGKDX5i4vW4BT-xmUNIvXQmbwOVovcFxbwnoiq3WqEt74bqBoRRQxJZrIVjYKvITPpqay8XdH9dgEaNKx-3V4BEXRMTS2mWB6HA/s1600/price6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="439" data-original-width="707" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFqa-pNOhYEheJSXrropkHos66CBxjYL3OJm-NVHpytGKDX5i4vW4BT-xmUNIvXQmbwOVovcFxbwnoiq3WqEt74bqBoRRQxJZrIVjYKvITPpqay8XdH9dgEaNKx-3V4BEXRMTS2mWB6HA/s640/price6.jpg" width="640" /></a></div>
<br />
For non-public transport, a <a href="https://www.ingentaconnect.com/content/lse/jtep/2001/00000035/00000002/art00001" target="_blank">study</a> by De Jong and Gunn reviews on evidence on <b>fuel elasticity</b>, with a focus on the EU. These are the most inelastic numbers we have seen so far. Which is probably not good news in terms of combating climate change.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinhyuecGtabapOVMdt7Qhapy9Igy2AF9GXBWfAb7k2wGpfnebpPUkVo2STTUA5Rjed2_eWnE00dT7bzdDulbRawexhRbtFczOU-cpDekRkwOO4C5lCvXDsJAfP4Me88iiBT13PG269f1k/s1600/price8.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="361" data-original-width="507" height="452" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinhyuecGtabapOVMdt7Qhapy9Igy2AF9GXBWfAb7k2wGpfnebpPUkVo2STTUA5Rjed2_eWnE00dT7bzdDulbRawexhRbtFczOU-cpDekRkwOO4C5lCvXDsJAfP4Me88iiBT13PG269f1k/s640/price8.jpg" width="640" /></a></div>
<br />
Talking of climate change, for <b>air-travel</b> there is a <a href="https://www.sciencedirect.com/science/article/abs/pii/S0969699701000503" target="_blank">meta-study</a> by Brons and co-authors. Overall travel is price elastic but business travel is not; no surprises there.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpklFdIT_yA0liippPb0iVl-B-_uDOMHJhy5iiwwStxmjPvANRYzZNrqZKx_e1w4NxQvz21yKwjuj2RUNFNW5SXIKbsZn4a2U9Eu-16RDJRd6t5BFQOGhkbaFKbaiLbsZgkKebdhgDYYk/s1600/price9.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="256" data-original-width="538" height="304" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpklFdIT_yA0liippPb0iVl-B-_uDOMHJhy5iiwwStxmjPvANRYzZNrqZKx_e1w4NxQvz21yKwjuj2RUNFNW5SXIKbsZn4a2U9Eu-16RDJRd6t5BFQOGhkbaFKbaiLbsZgkKebdhgDYYk/s640/price9.jpg" width="640" /></a></div>
<br />
Finally, a <a href="https://www.sciencedirect.com/science/article/pii/S0261517710001482" target="_blank">study</a> by Fleischer, Peleg and Rivlin looks at demand for <b>vacations</b> (by Israelis). Perhaps surprisingly you can see that demand is price inelastic.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMjQpoL3qqxFOH26lFuKkuiSn73ZMnHWpDhVBkuplc4RpEfcd1LFiVEKsL94fOv36oIRudlDPeGicTBCZuzQ6aXnDZl4dKTKiOSaqBn7-OJIRLynpzbM9Yroik15neJ3seuLWuGiKvh7Q/s1600/price10.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="371" data-original-width="485" height="305" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMjQpoL3qqxFOH26lFuKkuiSn73ZMnHWpDhVBkuplc4RpEfcd1LFiVEKsL94fOv36oIRudlDPeGicTBCZuzQ6aXnDZl4dKTKiOSaqBn7-OJIRLynpzbM9Yroik15neJ3seuLWuGiKvh7Q/s400/price10.jpg" width="400" /></a></div>
<br />
<br />
<br />
<br />
<br />
<br />
<br /></div>
<div style="text-align: justify;">
<br /></div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-82938514460776626502019-04-26T23:49:00.002-07:002019-04-26T23:49:26.894-07:00Is it ever optimal to play a mixed strategy?In the early days of its (modern) history game theory focused a lot on zero-sum games. These are games in which total payoffs always add to zero no matter what the outcome. So, in a two player setting - your gain is my loss and vice-versa. It was arguably natural for game theory to focus on zero-sum games because they represent the epitome of conflict. The main reason the focus fell on such games is, however, more one of convenience - zero-sum games have a <i>solution</i>.<br />
<br />
This solution is captured by the minimax theorem and all that followed. Basically it amounts to saying that there is a <i>unique way of playing a zero-sum game if all players want to maximize their payoff and are rational</i>. Most games do not have a 'solution', because there are multiple Nash equilibria and so there is not an obvious correct way to play the game. In this sense zero-sum games are 'nice' or 'convenient'.<br />
<br />
But does it make sense to behave according to the minimax theorem? The simple answer is no. This is because the theorem takes as given everyone is rational, and expects everyone to be rational. We know that in reality people are not rational, so why should you expect them to be. To illustrate the point consider a rock-scissors-paper game between Alice and Michael. The payoffs below are the payoffs of Alice.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcrLVFS1I2CfHABm1irueT30kNEKTzs0_EAd9FVuLdmMQxCvsW2Eoc_s04zSawI_6ALZfz_1aFfj4hpgbPc-BSSyC0bDk711BAvVPYuoqkceY_Q4HUj9XQisVn0SxPpnj1tYmZj3Q7lgo/s1600/rock.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="101" data-original-width="321" height="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcrLVFS1I2CfHABm1irueT30kNEKTzs0_EAd9FVuLdmMQxCvsW2Eoc_s04zSawI_6ALZfz_1aFfj4hpgbPc-BSSyC0bDk711BAvVPYuoqkceY_Q4HUj9XQisVn0SxPpnj1tYmZj3Q7lgo/s320/rock.jpg" width="320" /></a></div>
<br />
The essence of the 'solution' for Alice is that <i>her choice should not be predictable</i>. And, in a sense, this seems hard to argue with. If Alice is predictable in say, choosing Rock then Michael can pick this up and choose Paper. He wins. So, the solution is for Alice to randomly choose what she does in each play of the game. If she chooses randomly then she is unpredictable by definition.<br />
<br />
Randomization is good because it means Alice has a 50-50 chance of winning. But can Alice not do better? Seen in a different light randomization seems defeatist because it means Alice limits her ambitions to a 50-50 chance of winning. If she thinks she can see a pattern in Michael's behavior then should she not try and exploit that rather than continue to randomize? Yes.<br />
<br />
In reality we know that people are very poor at producing random sequences. So, if you are playing rock-scissors-paper it is highly unlikely your opponents strategy will be completely random. That opens the door for you to do better than 50-50. Note, however, that this means you are not randomizing either. Zero-sum games are not so much, therefore, about how well a person can randomize but more how well they can spot patters in another's behavior.<br />
<br />
Are there ever occasions where it makes sense to randomize? Taking a penalty kick in football, serving in tennis, playing poker? The answer seems no. Two absolute experts might just randomize and take their chances, consistent with the game theoretic 'solution'. But, in all likelihood your opponent will not be completely random and that means you shouldn't be either. You just <i>need to be better at predicting your opponent than he is of predicting you</i>.<br />
<br />
For an interesting analysis of how this can battle of prediction can be modeled and analyzed see the recent <a href="file:///C:/Users/Economcis/Downloads/games-10-00018.pdf" target="_blank">paper</a> by Dimitris Batzilis and co-authors in Games (MDPI). They use level-k theory to analyze choice in the rock-scissors-paper game. It is roughly the case that a player with a higher level of reasoning will win. And experience seems a key factor in level of reasoning.Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-40157186447589764252019-01-09T11:51:00.000-08:002019-01-09T11:51:54.512-08:00Have you heard of Berge equilibrium? And should you have?Recently I refereed a paper on the existence of Berge equilibrium. I must confess that until reading the paper I knew nothing of Berge equilibrium. But in my defence, the equilibrium does not get a mention in any game theory textbook on my shelves and, surely most telling of all, does not get an entry in Wikipedia. So, what is Berge equilibrium and should we hear more about it?<br />
<br />
The origins of the equilibrium are a book by French mathematician Claude Berge (who does get a Wikipedia page) on a general theory of n-person games, first published in 1957. But it has seemingly gone pretty much unnoticed from then on, although there is a growing literature on the topic as summarized in a 2017 <a href="http://www.mathnet.ru/links/3011b0bbbec620ad91068540b51296ad/iimi340.pdf" target="_blank">paper</a> by Larbani and Zhukovskii. The basic idea behind Berge equilibrium seems to be one of altruism or cooperation between players in a group.<br />
<br />
To explain, consider a game. Let s<span style="font-size: xx-small;">i</span> denote the strategy of player i, s<span style="font-size: xx-small;">-i</span> the strategies of everyone other than i and u<span style="font-size: xx-small;">i</span>(s<span style="font-size: xx-small;">i</span>, s<span style="font-size: xx-small;">-i</span>) the payoff of player i given these strategies.<br />
<br />
<b>Nash equilibrium</b> says that player i <i>maximizes his or her payoff</i> given the strategies of others. So, at a strict Nash equilibrium s<span style="font-size: xx-small;">i</span>*, s<span style="font-size: xx-small;">-i</span>* we have<br />
<br />
u<span style="font-size: xx-small;">i</span>(s<span style="font-size: xx-small;">i</span>*, s<span style="font-size: xx-small;">-i</span>*) > u<span style="font-size: xx-small;">i</span>(s<span style="font-size: xx-small;">i</span>, s<span style="font-size: xx-small;">-i</span>*) <br />
<br />
for all i and any other strategy s<span style="font-size: xx-small;">i</span>. This says that player i cannot do better by deviating.<br />
<br />
<b>Berge equilibrium</b> says that each player <i>maximizes the payoff of player i</i> given his or her strategy. So, at a strict Berge equilibrium s<span style="font-size: xx-small;">i</span>*, s<span style="font-size: xx-small;">-i</span>* we have<br />
<br />
u<span style="font-size: xx-small;">i</span>(s<span style="font-size: xx-small;">i</span>*, s<span style="font-size: xx-small;">-i</span>*) > u<span style="font-size: xx-small;">i</span>(s<span style="font-size: xx-small;">i</span>*, s<span style="font-size: xx-small;">-i</span>) <br />
<br />
for all i and for any other strategy s<span style="font-size: xx-small;">-i</span>. So, <b>the other players do their best to maximize the payoff of player i</b>.<br />
<br />
The differences between Nash equilibrium and Berge equilibrium are easy illustrated in the prisoners dilemma. In the game depicted below Fred and William simultaneously have to decide whether to deny or confess. Nash equilibrium says that Fred should Confess because this maximizes his payoff (whatever William does). Berge equilibrium, by contrast, says that Fred should Deny because this maximizes the payoff of William.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwMNp4VL5p7aQe94PY0Lcpu1J35lzuLEUR5ZctuNToFzu7BzIBq5egG9wUZQU5WMT8vpUNeEuFMZnghzcib5lO_JKMtm4QcumP_P0DNwgrBsdzAiqub4J9Q3FQz6in9b7Fgi9Yehfocbo/s1600/PD.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="137" data-original-width="511" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwMNp4VL5p7aQe94PY0Lcpu1J35lzuLEUR5ZctuNToFzu7BzIBq5egG9wUZQU5WMT8vpUNeEuFMZnghzcib5lO_JKMtm4QcumP_P0DNwgrBsdzAiqub4J9Q3FQz6in9b7Fgi9Yehfocbo/s400/PD.jpg" width="400" /></a></div>
<br />
Many have argued that Deny is the 'rational' choice in the prisoners dilemma (because both Deny is better than both Confess) and Berge equilibrium appears to capture that idea. Modern game theory, however, provides lots of ways to capture altruism or morality that are arguably more appealing. In particular we can add social preferences into the mix so that if Fred wants to help William then we put that into his payoff function. Then the prisoners dilemma (in material payoffs) is no longer a prisoners dilemma (in social preferences) because Fred maximizes his own payoff by Denying and helping William.<br />
<br />
Berge equilibrium only makes sense if <i>everyone</i> is willing to <i>fully sacrifice</i> for others, and that seems a long shot. Unless, that is, players have some connections beyond that usually imagined in non-cooperative game theory. In other words Berge equilibrium may have some bite if we move towards the world of cooperative game theory where Fred and William are part of some coalition. We could, for instance, imagine Fred and William being brothers, part of a criminal gang or players on the same sport team. Here it starts to become more plausible to see full sacrifice. And that it brings us to the concept of <b>team reasoning</b>.<br />
<br />
The basic idea behind team reasoning is that players think what is best for <i>us</i>. They act as a cohesive unit, like a family making choices. This looks similar to Berge equilibrium but is actually different. To see the difference consider the coordination game below. For both William and Fred to Cheat is a Berge equillibrium - given that Fred is going to cheat the best thing that William can do for Fred is also to cheat. But mutual Cooperation is clearly better (and also a Berge equilibrium). Team reasoning says unambiguously that both should Cooperate. So, team reasoning is arguably better at picking up sacrifice for the group cause.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizWBkeZH-xjjryHK4Wxh2AbIBidbj8ImiIRluAPaSxQ2Dk9Z6zmfil395Y5qw8uV-CCcwoHEMrnAkvCtaie1FEV_R7UJxOzMwetrEC3wlqkAqbvD-njx6XSVvS2PoUtttc3jlq4bp82ms/s1600/cooperation.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="95" data-original-width="420" height="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizWBkeZH-xjjryHK4Wxh2AbIBidbj8ImiIRluAPaSxQ2Dk9Z6zmfil395Y5qw8uV-CCcwoHEMrnAkvCtaie1FEV_R7UJxOzMwetrEC3wlqkAqbvD-njx6XSVvS2PoUtttc3jlq4bp82ms/s400/cooperation.jpg" width="400" /></a></div>
<br />
Given the tools we have to model social preferences and team reasoning I am skeptical Berge equilibrium will ever get beyond the level of an historical curiosity. But it is still interesting to know that such a concept exists.Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-46950130806327620502018-10-08T04:23:00.000-07:002018-10-08T04:27:29.851-07:00Reflections on the Rebuilding Macroeconomics Conference<br />
<div class="MsoNormal">
Last week I had the pleasure of attending the <a href="https://www.rebuildingmacroeconomics.ac.uk/2018-conference/" target="_blank">Rebuilding Macroeconomics Conference</a> with a theme of Bringing Psychology and Social
Sciences into Macroeconomics. The basic question of the conference seemed to be ‘how can we avoid another financial crisis’ or, from a different perspective, ‘how can we avoid not predicting the next financial crisis’. There was an impressive roll call of speakers from economics, psychology, anthropology, neuroscience, sociology, mathematics and so on with their own take on this issue. Here are a few random thoughts on the conference (with
the acknowledgement that I didn’t attend every session).</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
I was most at home with the talks from a behavioural
economics perspective. But it was still great to get extra insight on how this
work can be applied to macroeconomics. For instance, Rosemarie Nagel and Cars
Hommes gave an interesting perspective on how the beauty contest has real world
relevance. Most economists are familiar with the basic idea – people
individually write down a number, you find the average, multiple by 2/3 to get
the winning number, and being close to the winning number is good. No doubts
this is a great game to play in the lab to pick apart strategic reasoning and
learning. The new insight for me is how to connect the game directly with macro
behaviour. Basically, the world is one big beauty contest. Both Nagel
(focussing more on strategic reasoning) and Hommes (on learning) gave us a
picture of how to apply our knowledge of the beauty contest to inform macro
debate.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Still on familiar territory for me, David Laibson gave some
updated results on present bias. The main focus here is how we can explain the
average person simultaneously having a large credit card debt (at high interest)
and large savings (at low interest rates). The answer, according to Laibson, is
that we have present bias (and are naïve about it). This means we tend to focus
on today, putting off difficult things until tomorrow; until we get to tomorrow
and then we put it off until the next day. For connoisseurs of this the estimated
beta discount factor to explain observed bahaviour is 0.5; which basically means
today is a lot, lot more important than tomorrow. This implies that people are
going to put off things they should do, like save for retirement, and so there
is a remit and rationale for governments to come in and take some control of
important decisions.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Another session with a behavioural economics feel was panel
2 with talks by Sam Johnson and Henry Brighton. Johnson gave a great talk on
how people may fail to take into account ‘grey swan’ events. The basic idea
here is that the person thinks something is reasonably likely to occur, e.g.
there is a 20% chance Donald Trump will do a good policy, but when it comes to
making a decision they essentially ignore this possibility, they think there is
no chance Trump will do a good policy. This can lead to overconfidence or excess pessimism. The thing I would pick up on here is
that this presentation, like that of Laibson and others, emphasized some of the
‘dumb’ things humans do. Brighton, by contrast, gave the ecological rationality
viewpoint (most closely associated with Gerd Gigerenzer) that humans are
remarkably clever at making decisions. I think it is fair to say that Brighton
got a tough run in the subsequent discussion with a fairly hostile audience.
That surprised me a little because the ecological rationality argument surely
has some tractability. Maybe, however, in a conference on trying to avoid
another financial crisis the selling point of ‘don’t worry, humans are very
clever’ doesn’t seem to offer much of a solution.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
And that brings me to my main overall reflection on the
Conference, which is perhaps best summarized by ‘where were the
macro-economists?’. To be fair, there were some macro people in the room but
even they seemed unwilling to go far in defending DSGE modelling and the
current state of mainstream macro-economics. I am no macro-economist but I do
sense we may be reaching a turning point in the evolution of economic ideas. A turning point in which mainstream macro becomes
something of an irrelevance. There is no doubt that macro-economists will carry
on churning out mathematical models, publishing in top journals, and
celebrating their success. But is this stuff any use? Does it give us anything?
This conference was packed with people from other fields who arguably have more
to contribute when it comes to predicting the next financial crisis. Maybe
policy makers will start listening to them a bit more than the results of the
latest DSGE model? If so, that means we are entering a long period of flux
before a coherent new macroeconomics is born.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
To pick up on one example, I was particularly taken by the
role that anthropology can play. Douglas Holmes set the scene in looking at
central bank decision making. Then Charles Stafford gave a very compelling
argument that economists need to read anthropology. He used the example of
Taiwanese fisherman deciding whether to choose the high risk, financially
rewarding option or low risk, less rewarding option to illustrate the
complexities of decision making (and the role of religion). The title of his
talk ‘Economic life in the real world’ sums it up nicely. Economists can learn
from pocking their head above the simplicity of our mathematical models to see
what actually happens when people make economic decisions. But, lets be honest, it is a long step from conferences like this to building a new macro that incorporates such perspectives. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
And then we get to talk of Andrew Caplin which nicely drew
together various themes in the conference. Caplin reflected on his work about
bank runs financial crises before focussing on the theme of data. He argued
that a crisis typically comes about from a ‘predictable’ collapse in
confidence. Everyone is chugging along thinking things are bad but maybe it
will pick up; then one firm falls and everyone else falls with them. If we
could tap into people thinking ‘things are bad’ and understand the linkages
between firms then we would have the data to get on top of these things
earlier. But are we going to get data? Caplin explained that collecting this
data is going to require a long term, big team approach. And that is not what
economists are good at. He, therefore, was sceptical it will happen. Let’s hope
it does. Either way it seems that rebuilding macroeconomics may take some time. </div>
<br />
<br />
<div class="MsoNormal">
<o:p></o:p></div>
<br />Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-7236279973287012982018-09-08T23:25:00.000-07:002018-09-08T23:25:06.462-07:00Social value orientation in economics part 2 - slider method<div style="text-align: left;">
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;">In a previous <a href="http://econbeh.blogspot.com/2018/04/social-value-orientation-in.html" target="_blank">blog post</a> I looked at social vale orientation (SVO) and one method to measure it, namely the decomposed game or ring technique. Here I will look at a second way of measuring SVO called the <b>slider method</b>. This method, due to <a href="http://journal.sjdm.org/11/m25/m25.pdf" target="_blank">Ryan Murphy, Kurt Ackermann and Michel Handgraaf</a> is relatively new and has some nice advantages. While most existing studies use the ring technique I would expect the slider method to become the method of choice going forward. So, it is good to know how it works. </span></div>
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"><br /></span>
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;">Recall that the basic idea behind social value orientation (SVO) is to gain a snapshot of someone's social preferences. Are they </span><i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; text-align: justify;">selfish</i><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"> and simply do the best for themselves without caring about the payoff of others? Are they </span><i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; text-align: justify;">competitive</i><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"> and want to earn more than others (even if that means sacrificing own payoff)? Are they </span><i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; text-align: justify;">inequality averse</i><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"> and want to earn the same as others? Or are they </span><i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; text-align: justify;">pro-social</i><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"> and want to maximize the payoff of others? </span><br />
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"><br /></span>
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;">One way to categorize SVO is on a circle in which own payoff can be traded-off for that of another person. This is illustrated in the figure below. An altruist gives maximum to the other person, an individualist maximizes own payoff, a pro-social person maximizes joint payoff and a competitive person is willing to pay to lower the payoff of another person. Recall that the ring method asks someone to choose between 24 pairs of choices all around the circle. This allows us to categorize, in principle, where the person's preferences lie on the circle. But, the task is not that easy meaning that many subjects are going to make inconsistent choices etc.</span><br />
<br />
<div style="text-align: justify;">
<span style="color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"><span style="font-size: 13.2px;"><br /></span></span></div>
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"></span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlffPqdUc-0K4CHbG63H_cZr2EwHxc-_xCLvx52P4PYXFVcJFbvJNhhuG45Da3TUA8kbnQnc7igqPf3A24vavUbkr1qMzl5DFac83rtDptTtEr97oq6qe4PgcFMsU1azbth6r8zNt3hH4/s1600/SVOcategory.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="334" data-original-width="450" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlffPqdUc-0K4CHbG63H_cZr2EwHxc-_xCLvx52P4PYXFVcJFbvJNhhuG45Da3TUA8kbnQnc7igqPf3A24vavUbkr1qMzl5DFac83rtDptTtEr97oq6qe4PgcFMsU1azbth6r8zNt3hH4/s400/SVOcategory.jpg" width="400" /></a></span></div>
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The slider method gets straight to the heart of the matter by asking 6 questions that compare each pair of SVO categories. To illustrate, compare altruistic versus competitive. Suppose we draw a line between the altruistic choice of 50 for me and 100 for the other and the competitive choice of 85 for me and 15 for the other.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAN-_ZISsuN-FRM_44m1cITnP2fNL0pV5zPWVWanIIqn52jGqg4dRp_iUscfy2hifz5akwKtaZewLgclkJIiQ-lY12DKKvnuRiB6vAiJKdFIvy-JisXkUalswlR4PYGDAh6zlLNTNqfjk/s1600/SVO2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="334" data-original-width="450" height="295" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAN-_ZISsuN-FRM_44m1cITnP2fNL0pV5zPWVWanIIqn52jGqg4dRp_iUscfy2hifz5akwKtaZewLgclkJIiQ-lY12DKKvnuRiB6vAiJKdFIvy-JisXkUalswlR4PYGDAh6zlLNTNqfjk/s400/SVO2.jpg" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="" style="clear: both; text-align: left;">
We <span style="font-size: 13.2px; text-align: center;">can then ask a person where on that line they would choose to be. One of the slider method questions does just that. In the pen and paper version it could look like this.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUs1zcAwwYR-Wuvyd2UW_ijpV73gxfkgqdHomokkSSmiVrI4hlazES5XO-Tg0vYTQoxapucmYdxs-Ar14AjPgmZYJMJ2ZTrh8Wfo6Xn26wig_9Q6Mik9pFGBqcuU4Zha9rAYncmPrP18s/s1600/SVOQ4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="73" data-original-width="484" height="96" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUs1zcAwwYR-Wuvyd2UW_ijpV73gxfkgqdHomokkSSmiVrI4hlazES5XO-Tg0vYTQoxapucmYdxs-Ar14AjPgmZYJMJ2ZTrh8Wfo6Xn26wig_9Q6Mik9pFGBqcuU4Zha9rAYncmPrP18s/s640/SVOQ4.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;">The other combinations are altruist versus individualist, altruistic versus pro-social, pro-social versus individualist, pro-social versus competitive, and individualist versus competitive. That gives the 6 questions below. Combining the answers from the 6 questions gives an aggregate measure of where the person's preferences lie. Specifically, Murphy, Ackermann and Handgraaf suggest taking the average a person gives to self and the average given to other and measuring SVO by the resulting angle.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXayhGuyNwFRYnx6thedfyVTjI_7QsPQ3RG6NGoaPHzwYyz1FpsTj5vQDiK-XqqtkcxRYVMfRRuyM962RANznlzbSj8zXLtO5LK67fEcFoJ4OM0ztwco_YFdN6nB_0ppgKC6TAMU-laBs/s1600/svoComplete.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="481" data-original-width="706" height="435" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXayhGuyNwFRYnx6thedfyVTjI_7QsPQ3RG6NGoaPHzwYyz1FpsTj5vQDiK-XqqtkcxRYVMfRRuyM962RANznlzbSj8zXLtO5LK67fEcFoJ4OM0ztwco_YFdN6nB_0ppgKC6TAMU-laBs/s640/svoComplete.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;">For instance, consider the set of choices below over the 6 questions. The average amount given to self is 81.5 and that to other is 76.5. Subtracting 50 to normalize around 0 this gives a ratio of 0.84 = 26.5/31.5 and an angle of 40 degrees. This is someone who is pro-social. It should be said, however, that Murphy, Ackermann and Hangraaf are clearly not keen on putting boundaries between classifications but prefer the continuous measure given by the angle. Someone with an angle of 40 degrees is 'close' to the 'ideal' pro-social who would have 45 degrees.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2WpctQ675etlfz8unmxUdCFjDcXtn8d2x03ZcZsT6XLORgItlSrd56kG3UrGKqKAQDfvP0L-YW0Tpgta-cw6ciY8uZNiG1mjX5Dm2I1CIedrzxc95FKZcDp-TuR0l6EfjNeHIdJmFa6w/s1600/SVOsocial.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="469" data-original-width="485" height="386" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2WpctQ675etlfz8unmxUdCFjDcXtn8d2x03ZcZsT6XLORgItlSrd56kG3UrGKqKAQDfvP0L-YW0Tpgta-cw6ciY8uZNiG1mjX5Dm2I1CIedrzxc95FKZcDp-TuR0l6EfjNeHIdJmFa6w/s400/SVOsocial.jpg" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;">And that is the slider method. The beauty is its simplicity. This is a task subjects should be able to readily understand and can do relatively quickly. On this criterion it does better than the ring method. But the method also gives a continuous, detailed measurement. On this criterion it does better than other simple methods of eliciting SVO. So, there is a lot to like about the slider method! And, if necessary, another 9 questions can be used to distinguish between joint maximization and inequality aversion amongst pro-social types. </span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: 13.2px; text-align: center;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
The slider method is clearly something that could be used to good effect in experimental economics. Given how fresh it is there are not too many examples out there and many are still using the ring method. But, that will surely change. One recent study that does use the slider method is by Dorothee Mischkowski and Andreas Glockner on '<a href="https://www.nature.com/articles/srep21555" target="_blank">Spontaneous cooperation for prosocials, but not proselfs: Social value orientation moderates spontaneous cooperation behavior</a>'. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
They look at the spontaneous cooperation hypothesis that people's instinct is to cooperate. Given that the instinct is to cooperate, the longer a decision takes the less cooperation we will observe (because rationality takes over from instinct). Mischkowski and Glockner do indeed find that a longer decision time in a public good game correlates with lower contributions. The new insight is to show that this <i>only holds for pro-socials </i>as illustrated below. In this study pro-socials are those with an angle more than 22.45 degrees. So, if you want a nice person to do a nice thing - don't give them time to think about it. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE0vAFaAV2utYKrVmiuDHc5fOwqvrQ7toBfCSnwyQu_yFBqBBQ1xLznNUxe3WsnF90BWnTyq3akLcA0e0ba8kzcqEFFfxbOqHJaLQ6liyRe61EFpiYUQQdhIl5ffo1DZ6ucMK3ZFxdCYE/s1600/svoTime.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="660" data-original-width="926" height="285" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE0vAFaAV2utYKrVmiuDHc5fOwqvrQ7toBfCSnwyQu_yFBqBBQ1xLznNUxe3WsnF90BWnTyq3akLcA0e0ba8kzcqEFFfxbOqHJaLQ6liyRe61EFpiYUQQdhIl5ffo1DZ6ucMK3ZFxdCYE/s400/svoTime.jpg" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
</div>
</span><br />
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"></span><br />
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"><span style="font-size: 13.2px; text-align: center;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"><span style="font-size: 13.2px; text-align: center;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; text-align: justify;"><span style="font-size: 13.2px; text-align: center;"><br /></span></span></div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-12975227782496505652018-08-13T23:31:00.001-07:002018-08-13T23:31:56.905-07:00Don't panic. Loss aversion does exist.<div style="text-align: justify;">
A recent <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/jcpy.1047" target="_blank">paper</a> by David Gal and Derek Rucker in the <i>Journal of Consumer Psychology</i> sets out a strong critique of loss aversion - one of the most 'successful' and basic ideas in behavioural economics. So, do we really need to ditch loss aversion? Well the first thing to point out is that the paper by Gal and Rucker is considerably milder than a <a href="https://blogs.scientificamerican.com/observations/why-the-most-important-idea-in-behavioral-decision-making-is-a-fallacy/" target="_blank">blog-post</a> on Scientific American, by David Gal, that has got a lot of publicity. Personally, I would agree with a lot written in the paper but disagree with just about everything in the blog-post.<br />
<br />
So, what are the issues? Loss aversion says that losses loom larger than gains. In their paper, Gal and Rucker basically argue that losses do not always loom larger than gains. Fair enough. Indeed, this, of itself, is not particularly new. But, the 'standard' way of dealing with this 'problem' is to move around the reference point so that losses are no longer losses. For instance, Novemsky and Kahneman in a 2005 paper on '<a href="http://journals.ama.org/doi/abs/10.1509/jmkr.42.2.119.62292?code=amma-site" target="_blank">The boundaries of loss aversion</a>' highlighted contexts in which loss aversion may not kick in, and spending money on a planned purchase was one of those. Similarly, in looking at framing effects there is often considerably leeway to (re)define the reference point. This 'solution' of moving the reference point is not particularly convincing because it diminishes the predictive power of loss aversion and indeed could render it untestable. Gal and Rucker essentially argue we should do away with arbitrary movements in the reference point are recognize that losses are not always so bad.<br />
<br />
That all seems relatively uncontroversial. Things become a bit more controversial when it is implied, particularly in the blog post, that loss aversion is rarely an important factor. It is true that behaviour which is often attributed to loss aversion, like the endowment effect, may be due to something else, such as status quo bias. But does loss aversion exist? The answer surely has to be yes? For instance, in the blog-post it is said that 'people do not report their favorite sports team losing a game will be more impactful that their favorite sports team winning a game'. Well some very nicely done recent <a href="http://www.sussex.ac.uk/broadcast/read/44576" target="_blank">research</a> finds that football losses do indeed lead to an observable, deep and sustained drop in happiness! The evidence from the lab on $100 gain versus $100 loss is also pretty compelling. And in a way the paper does nothing to deny that. It just gives some examples where losses may not be considered worse than gains. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
To be useful, the concept of loss aversion (or prospect theory) does not rely on everyone being loss averse all of the time. It is enough that some people are <i>predictably</i> loss averse in certain contexts. And it is enough that the concept helps us predict and understand economic behaviour better than the alternative models. As a recent <a href="https://www.aeaweb.org/articles?id=10.1257/jep.32.2.91" target="_blank">paper</a> by Ted O'Donoghue and Jason Somerville point out loss aversion is probably the main reason we observe risk aversion (not diminishing marginal utility). This is a big shift in how we think about a core idea in economics. So, to find instances where loss aversion is not a factor is not to do away with all the instances where abundant evidence has shown loss aversion is a factor. This view would seem consistent with the basic theme in the paper of Gal and Rucker, but is hardly a novel one.<br />
<br />
Consider, for instance, the paper by Harrison and Rustrom, published in Experimental Economics, with the colourful title '<a href="https://link.springer.com/article/10.1007/s10683-008-9203-7" target="_blank">Expected utility theory and prospect theory: One wedding and a decent funeral</a>'. Basically, they say that some people might be expected utility maximizers - who are not loss averse - and some people might be prospect theorists - who are loss averse. They find that plenty of people are best described by prospect theory - more likely to be women, black or hispanic, and older students. Moreover, those that are best described by prospect theory have, on average, a huge loss aversion of factor 5. Yes, losses count 5 times as much as gains.<br />
<br />
Related results were obtained in a 2012 <a href="https://www.sciencedirect.com/science/article/pii/S0010027711002873" target="_blank">study</a> by Glockner and Pachur. They found that prospect theory fits better if we take account of individual heterogeneity. And once we take account of that heterogeneity we see that there is big variation in loss aversion. Some people appear to be strongly averse to losses and others not loss averse at all. This all seems consistent with the idea that loss aversion is useful without being some universal effect that always has the effect of doubling losses. (I'm essentially saying that Gal and Rucker, in claiming loss aversion is seen as universal, are setting up a straw man to make their point.)<br />
<br />
<div style="text-align: justify;">
So, should we ditch loss aversion? Of course not. A lot of people seem loss averse a lot of the time. Taking this into account improves the predictive power of economic models. Yes, we should be carefully to not overplay the importance of loss aversion, but I personally don't think we were doing that anyway. And lets face it, for an idea to survive the barrage of criticism hurled at behavioural economics over the last 30 plus years, it must have a grain of truth in it.</div>
</div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-88766773946317761782018-07-31T09:29:00.001-07:002018-07-31T09:29:03.254-07:00Experimental evidence on contagion and learning in networks<div style="text-align: justify;">
Using the workplace as an example, consider someone called Jane who interacts with different people over time on collaborative projects. For instance, this week she is working on a project with Sam, next week she is going to work on a project with David, the week after a project with Sam, and so on. The question of interest is whether her experience, say, working with Sam influences how she behaves when working with David? This, in turn, gives us some idea of how norms can emerge and evolve within a particular workplace. Can, for example, one slacker ruin productivity across a whole firm?</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
To make things more concrete suppose that the basic choice Jane has to make is how much effort to exert on a project. She can cooperate or slack. We can then think of a project as either a public good game or minimum effort game. In both games the best outcome for the group is mutual cooperation. The differences lie in individual incentives. In a public good game Jane maximizes her material payoff by slacking and so working hard basically requires her to be 'nice' (or forward looking to potential future gains). In the minimum effort game it is in Jane's interests to work hard if others on the project work hard and so the issue is more one of trust in others. We can now re-frame our question: Does bad experience on a project lower willingness to be nice and trust others on unrelated projects?<br />
<br />
For insight on this we can look to a 2013 <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1465-7295.2010.00332.x" target="_blank">paper</a> by Armin Falk, Urs Fischbacher and Simon Gachter published in <i>Economic Inquiry</i> on 'Living in two neighborhoods: Social interaction effects in the laboratory'. They randomly put subjects into a matching group of nine people. You can think of this as a workplace. A subject then interacted over time with two distinct groups of people within the matching group, as illustrated below. Here Jane is involved on a project with David and Robert and a distinct project with Sam and Freya. This set up allows us to nicely see if Jane's experience with, say, Sam influences how she behaves with David. The study considered both a public good game and minimum effort game.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAv3GNexVHgWu2_putQ5f812AdgLowZYhIaA-5VrQb8zJn_4IcbqKzPzgNX8BiZeLhhSqi6Vt19vNo99uCQNLy-jprtSjAILeJnE5e0Yih4uM_8DcY91IwWfnkIbOzDQZ-XQYvGAXIwYk/s1600/FFG-matching.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="133" data-original-width="305" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAv3GNexVHgWu2_putQ5f812AdgLowZYhIaA-5VrQb8zJn_4IcbqKzPzgNX8BiZeLhhSqi6Vt19vNo99uCQNLy-jprtSjAILeJnE5e0Yih4uM_8DcY91IwWfnkIbOzDQZ-XQYvGAXIwYk/s1600/FFG-matching.jpg" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
The main finding of the study was that subjects behavior <i>within</i> groups converged but not across groups. So, for example, Jane might converge on an equilibrium of high effort with Sam and Freya and one of slacking with David and Robert. This convergence within group suggests that people can freely adapt their behavior to the environment - cooperating with and trusting some colleagues and not others. This, in turn, suggests that contagion across the workplace may not be as pronounced as some would expect. If, for instance, David is a slacker the consequences can be contained to the projects he is involved with.<br />
<br />
In a recent study with Thomas Singh published in the <i>Journal of Behavioral and Experimental Economics </i>entitled 'Observation and contagion effects in cooperation' we find similar results. In our study subjects were in a matching group of 4 and paired off to play with each other. Again, we found that people were happy to adapt their behaviour to the person they were paired with - cooperating with one person and slacking with another. This, again, meant that behavior within group converged but not across groups.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK1FW2Dy647MgT2-oRbfrM4sKNRVouCDP3Lp-ZijlPhiZB0KCMQy2sb1_1uB_GBOOsFHKs3SFBkCCD3nBKwzoGALf2GY1g8L536KE5qJIKIoEARbqvyroLQW4-NknqQ34KjncPiMRvD70/s1600/CS-mathcing.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="130" data-original-width="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK1FW2Dy647MgT2-oRbfrM4sKNRVouCDP3Lp-ZijlPhiZB0KCMQy2sb1_1uB_GBOOsFHKs3SFBkCCD3nBKwzoGALf2GY1g8L536KE5qJIKIoEARbqvyroLQW4-NknqQ34KjncPiMRvD70/s1600/CS-mathcing.jpg" /></a></div>
We, though, added an extra factor into the mix by having treatments where subjects could see what others were doing. So, for instance, Jane can see what is happening on the projects Graham is involved with even though she does not directly interact with him. In the public good game this had no effect at all. In the minimum effort game, by contrast, it significantly <i>increased rates of cooperation</i>. Which is a good thing. Our design did not allow us to precisely disentangle why we get such an effect but we put it down to the cooperation of one group providing a focal point for others. Essentially, if Sam and Jane see Graham and David succeeding then they can more easily coordinate themselves.<br />
<br />
So, what are the lessons we can take from this? The results of these two studies and others suggest behaviour need not be contagious across groups. So, one slacker is not going to infect the whole workplace. But, equally, one hard worker is not going to dramatically boost the workplace. Observing others may, though, have a positive benefit. This is not so much conformity or 'blind' learning but more that success provides a focal point that can help others coordinate around. Let me finish by noting that a lot of the studies on networks (both theoretical and empirical) constrain a person to choose the same action in all interactions. So, Jane has to decide either to cooperate on all projects or slack on all projects. You can see that this is quite a strong (and potentially unrealistic) assumption.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<br /></div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-45594771999669581602018-06-08T06:30:00.000-07:002018-06-08T06:30:31.028-07:00Contestable markets: Can you have monopoly and perfect competition at the same time?<div style="text-align: justify;">
Last Sunday the sun was out and the children's playground was full of kids and their families. As usual the ice cream van was nearby with a steady stream of willing customers. Then something unexpected happening - another ice cream van turned into the car park. What would happen? Well, the driver saw he was not alone, turned around and left. So, we missed out on any particular excitement. Even so, this brief encounter is a nice illustration of the concept of contestable markets.</div>
<div style="text-align: justify;">
The standard textbook typically associates the extent of competition with the number of firms in the market. A monopoly has one firm and perfect competition has a large number of firms. Simple enough. But, also misleading, bordering on plain wrong. It is more accurate to measure competition, not by the number of firms, but by the restrictions on <i>entry</i> to the market and the <i>standardization</i> of goods in the market.</div>
<div style="text-align: justify;">
To illustrate the issues consider our ice cream van. Suppose the local council has a system for allocating a permit to operate near the playground. And they issue only <i>one</i> permit. Then the firm that gets the permit has monopoly power. That power comes from the fact that only they are allowed to operate - there are barriers to entry. In this scenario the ice cream van would be able to charge monopoly prices. For instance, suppose the marginal cost of selling an ice cream is £1.50. There is nothing to stop the monopolist charging say £2.00. Less people will buy for £2.00 than £1.50 but the net effect on profits may well be positive.</div>
<div style="text-align: justify;">
Now consider the scenario where anyone can come and set up an ice cream van near the playground. Moreover, suppose that there are no costs at all to doing this. Does the single ice cream seller still have monopoly power? No because if it charges more than £1.50 another ice cream van will soon come along and undercut. And, given the product is standardized nobody is going to buy an ice cream at, say, £2.00 if they can buy it next door for £1.75. The <i>threat </i>of competition, therefore, keeps prices at marginal cost. This is the basic notion of contestable markets.</div>
<div style="text-align: justify;">
Contestable markets mean that the number of sellers can be misleading. In particular, you could have only one seller but still have perfect competition. The one seller clearly satisfies the legal definition of monopoly because she has 100% market share. But the threat of entry means that she does not have market power to influence price. Hence, she does not meet the economic criteria for monopoly.</div>
<div style="text-align: justify;">
Clearly the idea of free entry to a market is unrealistic. For instance, it costs money and time to drive an ice cream van to the playground to check what is going on. That is a barrier to entry. Generally speaking, however, the lower the cost of entry the less power firms have to influence price. This is what really drives competition in the long run.</div>
<div style="text-align: justify;">
So, why do the textbooks focus on the number of firms? The number of firms may be a proxy for the ease of entry into the market. It is, however, not a perfect correlation. One can think of many contexts where a firm might have a large market share but if it were to push up prices too high someone else would come in and undercut. Moreover, a large number of firms in a market may be a sign of capacity constraints rather than lack of market power. Consider, for example, hotels and restaurants on a busy holiday weekend. There are lots of them but they can still hike up prices. </div>
<div style="text-align: justify;">
There is, though, particularly in the short run, a big difference between one firm in the market and two or more. That second firm makes a difference because it provides direct rather than threatened competition. Once you have two firms then a third has much less of an impact. Which is why it was somewhat disappointing the second ice cream van didn't set up shop and give some entertainment. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-89044508602076152212018-04-28T23:53:00.000-07:002018-04-28T23:53:29.371-07:00Social value orientation in experimental economics, part I<div style="text-align: justify;">
The basic idea behind social value orientation (SVO) is to gain a snapshot of someone's social preferences. Are they <i>selfish</i> and simply do the best for themselves without caring about the payoff of others? Are they <i>competitive</i> and want to earn more than others (even if that means sacrificing own payoff)? Are they <i>inequality averse</i> and want to earn the same as others? Or are they <i>pro-social</i> and want to maximize the payoff of others? SVO is a tool most closely associated with social psychology, but there is no doubt that it has a useful role to play in economics.<br />
<br />
A contribution that should be particularly interesting to economists is a recent <a href="https://onlinelibrary.wiley.com/doi/full/10.1002/per.2139" target="_blank">meta-analysis</a> published in the <i>European Journal of Personality</i> by Jan Luca Pletzer and co-authors. The analysis provides evidence on the connection between SVO, beliefs and behavior, which could feed into debates around reciprocity and psychological game theory. But I'm not going to talk about that study yet. Instead, I will do a couple of posts in which I explain different ways to measure SVO. Then I can get to the heart of why SVO can be useful for economists. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The first economics study I know of that used SVO was <a href="http://www.jstor.org/stable/2235360?seq=1#page_scan_tab_contents" target="_blank">published in 1996</a> by Theo Offerman, Jeop Sonnemans and Arthur Schram in the <i>Economic Journal</i>. There are many ways to elicit SVO. Here I will look in some detail at the approach they used, which is called the <b>decomposed game technique</b> or <b>ring technique</b>. To get us started consider the 24 different allocations in the table below. For instance, allocation a means $0 for yourself and $15 for some other person that you are matched with. Option b means $3.9 for yourself and $14.5 for the the other person, and so on. These 24 allocations neatly fit around a circle varying from a lot for both of you (allocation d) to not much for either of you (allocation p). </div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqGEmf97p5VP7mD3CQIUg-KivkEyCNDrkCObIeGMQlL9J6IjyFMTz_1Hly-LKBdfXBhK33xE5ScvAGIKGqsJcAWi8o_Wq4nW7PPnuCKbICcJLk61ExHc9FA_yOe1b0nJZWtyi99CylaW8/s1600/SVO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="509" data-original-width="650" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqGEmf97p5VP7mD3CQIUg-KivkEyCNDrkCObIeGMQlL9J6IjyFMTz_1Hly-LKBdfXBhK33xE5ScvAGIKGqsJcAWi8o_Wq4nW7PPnuCKbICcJLk61ExHc9FA_yOe1b0nJZWtyi99CylaW8/s1600/SVO.jpg" /></a></div>
<br />
<div style="text-align: justify;">
To elicit SVO subjects are given 24 decision tasks in which they need to choose between pairs of allocations from the circle. Specifically, they are asked if they would prefer allocation a or b, then if they would prefer b or c, then c or d, and so on, all around the circle. The slightly tricky thing is then converting those 24 choices into a measure of SVO. Here different studies take different approaches. The approach Offerman and co-authors take is to use the <i>observed motivational vector</i>. This works by adding up the total amount given to self and total amount given to other (over the 24 choices). From that we get a vector in the circle. The direction of that vector is used to measure value orientation.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The table below works through two examples. First we have an individualistic person who simply chooses whichever choice maximizes his own payoff. If you add up all his payoffs he overall gives 30 to himself and 0 to the other person. The angle this makes relative to the horizontal is 0 degrees. Next we have a cooperative person who makes 6 different choices, highlighted in yellow. In these 6 choices the individual sacrifices a little of his own payoff to the benefit of the other person. Ultimately both him and the other person end up with a total payoff of 21.2. This more pro-social behavior means the motivational vector is 45 degrees to the horizontal. </div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRswS2T4rw4O1gjWUjoYKL4cA6XWsixPbctClIQx02M878aPf7ra67pyTG1-Z6sdWOb94ONMBIpMYR5v95hmmulNHjHQrK8EyA5N2WOhKETfwvIZM8cbV9xVUV_qf_QCkmCVBK5dZ7iSs/s1600/SVO2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="543" data-original-width="992" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRswS2T4rw4O1gjWUjoYKL4cA6XWsixPbctClIQx02M878aPf7ra67pyTG1-Z6sdWOb94ONMBIpMYR5v95hmmulNHjHQrK8EyA5N2WOhKETfwvIZM8cbV9xVUV_qf_QCkmCVBK5dZ7iSs/s1600/SVO2.jpg" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
<br />
<div style="text-align: justify;">
Having worked out the angle of the observed motivational vector we can then classify SVO. (To work out the angle we need a bit of high school trigonometry, using arctan(other/self).) The figure below summarizes the classification. Anyone with a vector between -22.5 and 22.5 degrees is classified as individualistic - they care mainly about self. Anyone between 22.5 and 67.5 is classified as cooperative - these are somewhat pro-social towards others. While there are five categories in all it is individualistic and cooperative that matter most. For example, in the study by Offerman and co-authors, 65% of subjects were individualistic and 27% were cooperative. This split is fairly typical.</div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1CnxnSgKBR2wDBtTWL85WlRAfOyZGW6c6UdQ_hEzdC99BwJezcFMPp1m_cEP31doOlV-PEhjiHET5UgQ9BnocWbFd2y5eMRi88fzNdJm22yGXFCcbCByitdrLhycaBZGys_IBglYe3oc/s1600/SVO3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="384" data-original-width="418" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1CnxnSgKBR2wDBtTWL85WlRAfOyZGW6c6UdQ_hEzdC99BwJezcFMPp1m_cEP31doOlV-PEhjiHET5UgQ9BnocWbFd2y5eMRi88fzNdJm22yGXFCcbCByitdrLhycaBZGys_IBglYe3oc/s1600/SVO3.jpg" /></a></div>
<br />
<div style="text-align: justify;">
As I have already said, the method described above is only one of many ways to elicit SVO. But it is a relatively easy method for economists to use. And actually gives you two measures: the <i>angle</i> of the observed motivational vector allows you to classify SVO while the <i>length</i> of the vector gives you a measure of consistency of choice. The longer the vector the more consistent is the person to their classified SVO. Indeed, you sometimes find subjects who overall give 0 to themselves and 0 to the other person which suggests their choices are simply random.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So what to do with the SVO once you have it? I will come back to the issue looked at by Offerman and co-authors in a later post. Here I will look at a slightly simpler issue considered by Eun-Soo Park and <a href="https://www.sciencedirect.com/science/article/pii/S0167268100001281" target="_blank">published</a> in the <i>Journal of Economic Behavior and Organization</i>. Park looks at framing effects in public good games and the tendency for contributions to be higher in a positive frame - contribute and it benefits the group - than a negative frame - keep for yourself and it harms the group. By measuring SVO using the decomposed game technique Park finds that the framing effect is driven by individualistic types. The figure below illustrates how stark the effect was. With cooperative types there is no sign of any framing effect, but for individualistic types the effect is large. That finding can potentially give us important clues as to why we observe a framing effect. In particular, it suggests that selfish people can be induced to cooperate given the right frame.</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisbyYvSiRqFpK-GGbsaDKuN-z29_mEWLGp8vhVC-bjQqu4BfKEeTreErQqm3z8jpTOLtuYaShjExtPl3JAU1Z_lgGDu3rbl1HIcMDAAXJ_Qk8EdyLBcP2wAlBJoqO7AueI-TUbRa9W5Kg/s1600/ParkSVO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="537" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisbyYvSiRqFpK-GGbsaDKuN-z29_mEWLGp8vhVC-bjQqu4BfKEeTreErQqm3z8jpTOLtuYaShjExtPl3JAU1Z_lgGDu3rbl1HIcMDAAXJ_Qk8EdyLBcP2wAlBJoqO7AueI-TUbRa9W5Kg/s1600/ParkSVO.jpg" /></a></div>
<br />
<br />
<br />
<br />Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-13791686159684074732018-03-23T04:49:00.000-07:002018-03-23T04:51:24.893-07:00Cooperation in the infinitely (or indefinitely) repeated prisoners dilemmaOne of the more famous and intriguing results of game theory is that cooperation can be sustained in a repeated prisoners dilemma as long as nobody knows when the last game will be played. To set out the basic issue consider the following game between Bob and Francesca.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBPlMVuQ5OLheioIHEsvfeEB5kfAq2iEqKUJsHe9uggklTwGfjgwKBQn8O2vFpmd5RmXD19bn7S8NU8b2l9XT3QrjZHP_2ewWkBNQKi4hk6O2sgSZHOPeZlsayoQG_ExmEzdV7MU7y1zQ/s1600/PD.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="81" data-original-width="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBPlMVuQ5OLheioIHEsvfeEB5kfAq2iEqKUJsHe9uggklTwGfjgwKBQn8O2vFpmd5RmXD19bn7S8NU8b2l9XT3QrjZHP_2ewWkBNQKi4hk6O2sgSZHOPeZlsayoQG_ExmEzdV7MU7y1zQ/s1600/PD.jpg" /></a></div>
<br />
If they both cooperate they get a nice payoff of 10 each. If they both defect they get 0 each. Clearly mutual cooperation is better than mutual defection. But, look at individual incentives. If Francesca cooperates then Bob does best to defect and get 15 rather than 10. If Francesca defects then Bob does best to defect and get 0 rather than -5. Bob has a dominant strategy to choose defect. So does Francesca. We are likely to end up with mutual defection.<br />
<br />
But what if Bob and Francesca are going to play the game repeatedly with each other? Intuitively there is now an incentive to cooperate in one play of the game in order to encourage cooperation in subsequent plays of the game. To formalize that logic suppose that whenever Bob and Francesca interact then with probability p they will interact again tomorrow. Also suppose that both Bob and Francesca employ a grim trigger strategy - I will cooperate unless you defect and if you defect I will defect forever after. Can this sustain cooperation?<br />
<br />
If Bob and Francesca cooperate in every play of the game the expected payoff of Bob is 10 for as long as they keep on playing, which gives<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVozRqLKmocZciZHILzZk-qkjKqoPkx2dVKTOgFAtNEkdU-Ws8XF8MZX4ascj436AhFTpVOWx-BDyHjhXryuGvYQl37EM25NBfmH__HDLWzj6DmDM1UaSJvmdxzXEgeieIgWc6Hq1nT4k/s1600/PDeq1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="37" data-original-width="246" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVozRqLKmocZciZHILzZk-qkjKqoPkx2dVKTOgFAtNEkdU-Ws8XF8MZX4ascj436AhFTpVOWx-BDyHjhXryuGvYQl37EM25NBfmH__HDLWzj6DmDM1UaSJvmdxzXEgeieIgWc6Hq1nT4k/s1600/PDeq1.jpg" /></a></div>
If Bob defects now his expected payoff is 15 because he gets a one time benefit and then has to settle for mutual defection from then on. It follows that cooperating makes sense if 10/(1 - p) > 15 or p > 0.33. It should be emphasized that this story relies on Bob and Francesca both using a grim trigger strategy and both expecting the other to use it. Even so, cooperation can, in principle, be sustained if p is high enough. By contrast, if people know when the end is likely to come (p is small) then there is no hope of sustaining cooperation.<br />
<br />
What of the evidence? A <a href="https://www.aeaweb.org/articles?id=10.1257/jel.20160980" target="_blank">paper</a> recently published by Pedro Dal Bo and Guillaume Frechette in the <i>Journal of Economic Literature</i> surveys the evidence. They fit a model to a meta-data set of over 150,000 choices from relevant studies. The Figure below summarizes some of the findings that come out of that model. In interpreting this figure we need to understand that in most experiments subjects play the repeated game several times against different opponents. So, Bob plays with Francesca for, say, 10 rounds (determined randomly according to p). This is supergame 1. He then plays with Claire for, say, 5 rounds (again randomly determined according to p). This is supergame 2. And so on.<br />
<br />
The figure below shows the fitted probability of a subject cooperating in round 1 of supergame 1 and of round 1 of supergame 15. Look first at supergame 1. Here we can see that around 50-60% of subjects cooperate - which is quite high - and the probability of cooperating does <i>not</i> depend much on p. This is inconsistent with the theory because we would not expect such high levels of cooperation when p is low. What about in supergame 15? Here we see a much higher dependence on p. This is starting to look more consistent with the theory because we see low levels of cooperation when p is low. <br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia2fZ67FBXv4AJZ5zivs9SC918Cxzw4848XHFqHSWOorycAmJMlyNHtz_8Zc6i2jBHkJNv_0DQhCImDmhrrz-gzJ6BNar5iE3GOufTTfGCp9-29KfQg9LGKLyG398QNwFLMLnPqiJlwBg/s1600/cooperation.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="288" data-original-width="480" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia2fZ67FBXv4AJZ5zivs9SC918Cxzw4848XHFqHSWOorycAmJMlyNHtz_8Zc6i2jBHkJNv_0DQhCImDmhrrz-gzJ6BNar5iE3GOufTTfGCp9-29KfQg9LGKLyG398QNwFLMLnPqiJlwBg/s400/cooperation.png" width="400" /></a></div>
<br />
So, can cooperation be sustained in a repeated prisoners dilemma? The relatively high levels of cooperation seen in the above figure may give some optimism. But it is important to appreciate that cooperation is only going to be sustained if <i>both</i> people cooperate. If there is a 50% chance a random individual will cooperate then there is only a 25% chance they will start with mutual cooperation. This does not look so good. And it turns out that 'always defect' consistently shows up as the most popular strategy employed when playing the prisoners dilemma. The chances of sustained cooperation among two strangers seem, therefore, somewhat remote.<br />
<br />
All hope, though, is not lost because life is not only about interaction between strangers. Once we add in reputation, choosing who your friends are, and so on, there are various mechanisms that may be able to sustain cooperation. And, even putting that aside, there are still strong arguments to try and cooperate with strangers. As David Kreps, Paul Milgrom, John Roberts and Robert Wilson pointed out in a <a href="https://www.sciencedirect.com/science/article/pii/0022053182900291" target="_blank">well-cited paper</a> it is not always in your interest to defect in the first round of a prisoners dilemma. Basically, if the other person wants to be cooperative then by defecting you miss out long term. Better to cooperate and give the other person a chance.Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-47767795444440488562018-02-28T06:51:00.001-08:002018-02-28T06:51:47.234-08:00How many subjects in an economic experiment?<div style="text-align: justify;">
How many subjects should there be in an economic experiment? One answer to that question would be to draw on power rules for statistical significance. In short, you need enough subjects to be able to reasonably reject the null hypothesis you are testing. This approach, though, has never really been standard in experimental economics. There are two basic reasons for this - practical and theoretical. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
From a practical point of view the power rules may end up suggesting you need a lot of subjects. Suppose, for instance, you want to test cooperation within groups of 5 people. Then the unit of observation is the group. So, you need 5 subjects for 1 data point. Let's suppose that you determine you need 30 observations for sufficient power (which is a relatively low estimate). That is 30 x 5 = 150 subjects per treatment. If you want to compare 4 treatments that means 600 subjects. This is a lot of money (at least $10,000) and also a lot of subjects to recruit to a lab. In simple terms, it is not going to happen. </div>
<br />
That my appear to be sloppy science but there is a valid get-out clause. Most of experimental economics is about testing a theoretical model. This allows for a Bayesian mindset in which you have a prior belief about the validity of the theory and the experimental data allows you to update that belief. The more subjects and observations you have the more opportunity to update your beliefs. But even a small number of subjects is useful in updating your beliefs. Indeed, some of the classic papers in experimental and behavioral economics have remarkably few subjects. For instance, the famous Tversky and Kahneman (1992) <a href="https://link.springer.com/article/10.1007/BF00122574" target="_blank">paper on prospect theory</a> had only 25 subjects. That did not stop the paper becoming a classic.<br />
<br />
<div style="text-align: justify;">
Personally I am a fan of the Bayesian mindset. This mindset doesn't, though, fit comfortably with how economic research is typically judged. What we should be doing is focusing on a body of work in which we have an accumulation of evidence, over time, for or against a particular theory. In practice research is all too often judged at the level of a single paper. That incentivizes the push towards low p values and an over-claiming of the significance of a specific experiment. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Which brings us on to the <a href="http://www.sciencemag.org/news/2016/03/about-40-economics-experiments-fail-replication-survey" target="_blank">replication crisis</a> in economics and other disciplines. A knee-jerk reaction to the crisis is to say we need ever-bigger sample sizes. But, that kind of misses the point. A particular experiment is only one data point because it is run with a specific subject pool using a specific protocol. Adding more subjects does not solve that. Instead we need replication with different subject pools under different protocols - the slow accumulation of knowledge. And we need to carefully document research protocols.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
My anecdotal impression is that journal editors and referees are upping the ante on how many subjects it takes to get an experiment published (without moving things forward much in terms of documenting protocols). To put that theory to a not-at-all scientific test I have compared the papers that appeared in the journal <i>Experimental Economics</i> in its first year (1998) and most recent edition (March 2018). Let me emphasize that the numbers here are rough-and-ready and may well have several inaccuracies. If anyone wants to do a more scientific comparison I would be very keen to see it. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Anyway, what do we find? In 1998 the average number of subjects was 187, which includes the study of Cubbit, Starmer and Sugden where half the population of Norwich seemingly took part. In 2018 the average is 383. So, we see an increase. Indeed, only the studies of Cubbit et al. and Isaac and Walker are above the minimum in 2018. The number of observations per treatment are also notably higher in 2018 at 46 compared to 1998 when it was 16. Again, those numbers are almost certainly wrong (for instance the number of independent observations in Kirchler and Palan is open to interpretation). The direction of travel, though, seems clear enough. (It is also noticeable that around half of the papers in 1998 were survey papers or papers reinterpreting old data sets. Not in 2018.) </div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz5b3cWCj3XRtV8s06yuou3JMER9FuiJOzGZSL1N7GrxMcNcBnRKsZhnV61WyVGwBTQvXss0gFN0LkSoZnNcYwbI7VW2fghv3060GWx99SXBfeZDtqMVrurzqwyUtEkb-vcoYvtbBq84g/s1600/observations.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="421" data-original-width="580" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz5b3cWCj3XRtV8s06yuou3JMER9FuiJOzGZSL1N7GrxMcNcBnRKsZhnV61WyVGwBTQvXss0gFN0LkSoZnNcYwbI7VW2fghv3060GWx99SXBfeZDtqMVrurzqwyUtEkb-vcoYvtbBq84g/s400/observations.png" width="400" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
At face value we should surely welcome an increase in the number of observations? Yes, but only if it does not come at the expense of other things. First we need to still encourage replication and the accumulation of knowledge. Experiments with a small number of subjects can still be useful. And, we also do not want to create barriers to entry. At the top labs running an experiment is relatively simple - the money, subject pool, programmers, lab assistants, expertise etc. are there and waiting. For others it is not so simple. The more constraints we impose for an experiment to count as 'well-run' the more experimental economics may potentially become 'controlled' by the big labs. If nothing else, that poses a potential problem in terms of variation in subject pool. Big is, therefore, not necessarily better. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-2393469973419780332018-01-28T09:04:00.000-08:002018-01-28T09:04:14.692-08:00Would you want to be an expected utility maximizer<div style="text-align: justify;">
I have finally got around to reading Richard Thaler's fantastically wonderful book on <i>Misbehaving</i>. One thing that surprised me in the early chapters is how Thaler backs expected utility theory as the <i>right way to think</i>. Deviations from expected utility are then interpreted as humans not behaving 'as they should'. While I am familiar with this basic argument it still came as a surprise to me how firmly Thaler backed expected utility theory. And I'm not sure I buy this argument. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
To appreciate the issue consider some thought experiments. Thaler gives the following example:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<i>Stanley mows his lawn every weekend and it gives him terrible hay fever. I ask Stan why he doesn't hire a kid to mow his lawn. Stan says he doesn't want to pay the $10. I ask Stan whether he would mow his neighbor's lawn for $20 and Stan says no, of course not.</i><br />
<br /></div>
<div style="text-align: justify;">
From the point of view of expected utility theory Stan's behavior makes no sense. What we should do is calculate the recompense Stan needs to mow a lawn. That he will not pay the kid shows that he values $10 more than mowing a lawn. That he will not mow his neighbor's lawn shows that he does not value $20 more than mowing his lawn. But how can mowing a lawn be worth less than $10 and more than $20. It cannot! His choice makes no sense.</div>
<div style="text-align: justify;">
<span style="font-family: inherit;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: inherit;">Here is another example (which I have adapted a bit):</span><br />
<div style="color: black; font-weight: 400; letter-spacing: normal; text-align: justify; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">
<div style="font-style: normal; margin: 0px;">
<span style="font-family: inherit;"><br /></span></div>
<div style="margin: 0px;">
<i><span style="font-family: inherit;">Morgan got free tickets to a high profile NBA basketball game. Tickets are selling on the legal second hand market for $300. Morgan says that he is definitely going to the game. Asked if he would pay $200 for a ticket he says 'of course not'.</span></i></div>
</div>
</div>
<div style="text-align: justify;">
<br />
Again, from the point of expected utility theory Morgan's choices are nonsense. What we should do here is ask how much he values going to the game. He explicitly says that he would not be willing to pay $200. Yet by going to the game he misses out on selling his tickets for $300. So, it looks as though he values the game more than $300. But how can going to the game be worth less than $200 and more than $300. It cannot! His choices also make no sense. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
What to do with these two examples. The key question is this: <i>Do you think Stanley and Morgan would change their choices if the 'irrationality' of their choices are explained to them?</i> Personally, I think not. To them their behavior probably seems perfectly sensible, and who are we to argue against that? One response to this would be to 'add on' factors that influence preferences such as 'I prefer mowing my own lawn' or 'I don't like giving away tickets'. This can rescue expected utility theory but is precisely the kind of ad-hocness that behavioral economics is trying to get away from. So, I think it is just better to accept that expected utility is not necessarily the right way to make decisions.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Does this matter? Mainstream economics is built upon the premise that expected utility theory is a good representation of how people <i>make</i> decisions. The work of Thaler and others has blown that idea out of the water. So, whether or not expected utility is the right way to do things is rather a mute point. There is still merit in learning how a person should behave if their preferences satisfy certain basic axioms. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Things are more complicated when we look at the heuristics and biases approach led by Daniel Kahneman and Amos Tversky. Here the <i>biases</i> suggests that there is a right way to do things! It is worth clarifying, however, that much of this work relates to probabilistic reasoning where there is a clearly defined right way of doing things. I suggest that we just have to be a bit careful extending the biases terminology to choice settings where there may not be a right way of doing things. For instance, is loss aversion a bias? Put another way, is it irrational to behave in one way when things are framed as losses and another way when the same choice is framed in terms of gains? It is certainly different to how economists have traditionally modeled things. But it still seems perfectly sensible to me (and may make evolutionary sense) that someone could be influenced by the frame. Maybe, therefore, we need to call it the status-quo-effect rather than status-quo-bias. This, though, is surely more of a matter of semantics rather than anything particularly substantive.<br />
<br />
Things are also a bit complicated when we come to policy interventions. For instance, the nudge idea kind of suggests there is a right way of doing things that we can nudge people towards. But then there are so many situations where people make unambiguously bad choices (like saving for retirement) that we can still be excited about nudge without getting too caught up on whether expected utility theory is <i>always</i> the best way to make decisions. And remember the basic idea behind nudge is that we should never restrict choice anyway.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So, whether or not it is rational to maximize expected utility is probably not a big issue. It just means, to use Thaler's well known terminology, that: Humans may not be quite as dumb as Thaler claims, but they are undeniably very different to the Econs you find in a standard textbook.</div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-17070973538839647472017-12-30T01:28:00.000-08:002017-12-30T01:28:42.567-08:00Behavioral economics or experimental economics<div style="text-align: justify;">
My holiday reading started with the book <a href="http://www.cambridge.org/gb/academic/subjects/economics/history-economic-thought-and-methodology/behavioral-economics-history?format=PB#Wx6FG0vVwClutVYe.97" target="_blank">Behavioral Economics: A History</a> by Floris Heukelom. The book provides a interesting take on how behavioral economics has grown from humble beginnings to the huge phenomenon that it now is. A <a href="http://journals.openedition.org/oeconomia/1498" target="_blank">nice review</a> of the book has been written by Andreas Ortmann and so I will not delve too deeply into general comment here, other than to say I enjoyed reading the book. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
But in terms of more specific comment, one theme running throughout the book is the distinction between behavioral economics and experimental economics. Heukelom makes clear that he thinks there is a very sharp distinction between these two fields. Personally I have always thought of them both as part of one big entangled blob. There are people who clearly prefer to label themselves a behavioral economist or an experimental economist but this seemed to me more a matter of personal preference than any grand design. So, what is the difference between behavioral and experimental economics?<br />
<br />
Heukelom's viewpoint is based on a very narrow definition of experimental economics and behavioral economics. Specifically, he associates experimental economics with the work of Vernon Smith on experimental asset markets and he associates behavioral economics with the work of Kahneman, Tversky and Thaler, particularly with regard to prospect theory. The gap between research on market efficiency in the lab and that on prospect theory is indeed large. For instance, the first is more focused on market institutions and ecological rationality (i.e. how do markets work) while the later is focused on individual decision making and individual rationality (i.e. how do people behave). So, here a neat dividing line does potentially exist.<br />
<br />
The problem with this view is that experimental asset markets are, and long have been, only one small part of work that must surely fall under the umbrella of experimental economics. (See, for instance, the <a href="https://stanford.edu/~alroth/history.html" target="_blank">short summary</a> on the early years of experimental economics by Alvin Roth.) Similarly, prospect theory is only one small part of work that must fall under the umbrella of behavioral economics. For example, one elephant in the room here is game theory. From its very beginnings game theory has had an experimental side which has grown alongside work on markets. For instance, experiments with the prisoners dilemma and social dilemmas more generally began in the 1950s, if not before, and are generally seen as a big part of experimental economics. Similarly, a big part of behavioral economics has been to understand social preferences and move away from the standard economic assumption of selfishness. Indeed, the dictator game, which is now a mainstay of experimental economics, was first used by Kanheman, Knetsch and Thaler in a <a href="https://www.jstor.org/stable/2352761" target="_blank">paper published in 1986</a>.<br />
<br />
In short, everything is mixed up. Other ways of trying to find a neat dividing line between behavioral and experimental economics would also seem doomed to end up with a mess. For instance, at the end of the book Heukelom associates modern behavioral economics with the use of mathematical methods. But that would seemingly exclude a host of behavioral economics, Dan Ariely to name just one, whose work is not particularly characterized by the use of mathematics. Similarly, experimental economists, like Robert Sugden and Chris Starmer, have been prominent in recent developments in prospect theory. <br />
<br />
This is not to say that experimental and behavioral economics are the same. Experimental economics is characterized by a method of doing things - namely experiments - while behavioral economics (although much harder to tie down) is more characterized by an objective to understand how people reason in economic contexts. The trouble is it is hard to see how the one can be done without the other. Pushed to the limits it may be possible to study experimental markets without being bothered with individual behavior. Or to work on individual behavior without recourse to lab or field experiments. The truth, though, is surely that the two go very much hand in hand and, given that we are talking about the history of behavioral economics, always have done. <br />
<br />
An interesting question is how things will develop in the future. Both the terms experimental and behavioral economics are essentially referring to methods. In the infancy of something like experimental economics it is natural that someone doing experiments would use a label like experimental economics to distinguish what they are doing. But the more routine it becomes for the 'average' economist to use experiments or draw on behavioral theory the less relevant the labels would seem to be. Instead we could gravitate towards a focus on applications with more use of the labels like public, labor and development economics. Behavioral economics is, though, presumably too much of a buzz phrase for that to happen any time soon. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-88587967715447696202017-11-08T00:53:00.000-08:002017-11-08T00:53:05.416-08:00Rank dependent expected utility<div style="text-align: justify;">
Prospect theory is most well known for its assumption that gains are treated differently to losses. Another crucial part of the theory, namely that probabilities are weighted, typically attracts much less attention. Recent evidence, however, is suggesting that probability weighting has a crucial role to play in many applied settings. So, what is probability weighting and why does it matter?</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The basic idea of probability weighting is that people tend to overestimate the likelihood of events that happen with small probability and underestimate the likelihood of events that happen with medium to large probability. In their famous paper on '<a href="https://link.springer.com/article/10.1007%2FBF00122574?LI=true" target="_blank">Advances in prospect theory</a>', Amos Tversky and Daniel Kahneman quantified this effect. They fitted experiment data to equation<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0lX1RlpQ8ARlRJ0akXD7yqf-fFx7Ds6JCQeEfYUUGoq4DLZ_fmgjWgWJ_A2SdABd01pP3VqnVRq0xpLrUGKNGk87ULc5DGUGVXa9u70edrFsQUOgrNKdeyYH27Kv2VcmUcOyLlt59Rkk/s1600/weighting.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="49" data-original-width="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0lX1RlpQ8ARlRJ0akXD7yqf-fFx7Ds6JCQeEfYUUGoq4DLZ_fmgjWgWJ_A2SdABd01pP3VqnVRq0xpLrUGKNGk87ULc5DGUGVXa9u70edrFsQUOgrNKdeyYH27Kv2VcmUcOyLlt59Rkk/s1600/weighting.jpg" /></a></div>
<br />
where <span style="font-family: "Cambria Math"; font-size: 11pt;">γ </span>is a parameter to be estimated. In interpretation, p is the actual probability and <span style="font-family: "Cambria Math"; font-size: 11pt;">π</span><span style="font-family: "Cambria Math"; font-size: 11pt;">(p) </span>the weighted probability. The figure below summarizes the kind of effect you get. Tversky and Kahneman found that a value of <span style="font-family: "Cambria Math"; font-size: 14.6667px;">γ </span>around 0.61 best matched the data. This means that something which happens with probability 0.1 gets a decision weight of around 0.2 (overweighting of small probabilities) while something that happens with probability 0.5 gets a decision weight of only around 0.4 (underweighting of medium to large probabilities). </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZBeO-m_ZXv38uVEmtXWlh2nBGgBn8RjKg0vS9vIGr0fNONrRijZhCp3aZtwiV1rLodUNsHy5i4zLVE2c_nGLzWHgwohQS5kSWg7HLedYomcdqRmoZcKfuzcQ1bMLGXiBjYSutGRAzc9I/s1600/weighting.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="447" data-original-width="719" height="247" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZBeO-m_ZXv38uVEmtXWlh2nBGgBn8RjKg0vS9vIGr0fNONrRijZhCp3aZtwiV1rLodUNsHy5i4zLVE2c_nGLzWHgwohQS5kSWg7HLedYomcdqRmoZcKfuzcQ1bMLGXiBjYSutGRAzc9I/s400/weighting.jpg" width="400" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Why we observe this warping of probabilities is unclear. But the consequences for choice can be important. To see why consider someone deciding whether to take on a gamble. Their choice is either to accept £10 for certain or gamble and have a 10% chance of winning £90 and a 90% chance of winning nothing. The expected value of this gamble is 0.1 x 90 = £9. So, it does not look like a good deal. But, if someone converts a 10% probability into a decision weight of 0.2 we get value 0.2 x 90 = £18. Suddenly the gamble looks great! Which might explain the appeal of lottery tickets.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
There is, though, a problem. It is not enough to simple weight all probabilities. This, as I will shortly explain, doesn't work. So, we need some kind of trick. While prospect theory was around in 1979 it was not until the early 1990's that the trick was found. That trick is rank dependent weighting. The gap of over 10 years in finding a way to deal with probabilities may help explain why probability weighting has had to play second fiddle to loss aversion. Lets, though, focus on the technical details.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Consider the example. Here there are no obvious problems if we just weight probabilities. The 10% chance of winning is converted into a 0.2 decision weight while the 90% chance of losing is converted into a 0.7 decision weight. The overall expected value is then 0.2 x £90 = £18. Everything looks fine.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So, consider another example. Suppose that the sure £10 is now a gamble with a 10% chance of winning £10.09, a 10% chance of winning £10.08, a 10% chance of winning £10.07, and so on, down to a 10% chance of winning £10. If we just simply weight all these 10% probabilities as 0.2 then we get expected value of 0.2 x 10.09 + 0.2 x 10.08 + ... + 0.2 x 10 = £20.09. This is absurd. A gamble that essentially gives £10 cannot be worth over £20! You might say that the problem here is we have ended up with a combined weight of 2. If, though, we normalize weights to 1 we will not have captured the over-weighting of small probabilities. So, normalizing is not, of itself, a solution. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The problem with the preceding approach is that we have weighted everything - good or bad - by the same amount. Rank dependent probability does away with that. Here we rank outcomes from best to worst. The decision weight we place on an outcome is then the <i>weighted probability of the outcome or something better minus the weighted probability of something better</i>. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In our original gamble the best outcome is £90 and the worst is £0. The weight we put on £90 is around 0.2 because there is 10% chance of £90, no chance of anything better, and a 10% probability is given weight 0.2. The weight we put on £0 is 0.8 because it is the weighted probability of £0 or better, namely 1, minus the weighted probability of £90, namely 0.2. So, not much changes in this example.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In the £10 gamble the best outcome is £10.09, the next best £10.08, and so on. The decision weight we but on £10.09 is around 0.2 because there is a 10% chance of £10.09 and no chance of anything better. Crucially, the weight we put on £10.08 is only around 0.1 because we have the weighted probability of £10.08 <i>or better</i>, a 20% chance that gives weight around 0.3, minus the weighted probability of £10.09, around 0.2. You can verify that the chance of winning £10.07, £10.06 and so on has an even lower decision weight. Indeed, decision weights have to add to 1 and so the high weight on £10.09 is compensated by a lower weight on other outcomes. For completeness the table below gives the exact weights you would get with the Tversky and Kahneman parameters. Given that decision weights have to add to 1 the expected value is going to be around £10. Common sense restored!</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYYGFwuUsBl7lpFZl8Qz4mCefXak4s5UXuaGgIPDN9ttxOoK0WwLHxnMNOs-dSOiFSOxx58y74jXSH7OTJHLAMWKQULgQ9BVbSdGoHANv20GqI7BBIEDZ3YA3NWRXMVVi6QcE8Mpvq-yQ/s1600/exactWeights.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="268" data-original-width="257" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYYGFwuUsBl7lpFZl8Qz4mCefXak4s5UXuaGgIPDN9ttxOoK0WwLHxnMNOs-dSOiFSOxx58y74jXSH7OTJHLAMWKQULgQ9BVbSdGoHANv20GqI7BBIEDZ3YA3NWRXMVVi6QcE8Mpvq-yQ/s1600/exactWeights.jpg" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Generally speaking, rank dependent weighting means that we capture, and only capture, over-weighting of the extreme outcomes. So, we capture the fact a person may be overly optimistic about winning £90 rather than £0 without picking up the perverse prediction that <i>every</i> unlikely event is over-weighted. The discussion so far has focused on gains but we can do the same thing with losses. Here we want to capture, and only capture, over-weighting of the worst outcomes. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So why does all this matter? There is mounting evidence that weighting of probabilities can explain a lot of behavior, including the equity premium puzzle, long shot bias in betting and willingness of households to buy insurance at highly unfavorable premiums. For a review of the evidence see the article by Helga Fehr-Duda and Thomas Epper on '<a href="http://www.annualreviews.org/doi/full/10.1146/annurev-economics-080511-110950" target="_blank">Probability and risk: Foundations and economic implications of probability-dependent risk preferences</a>'. It is easy to see, for instance, why overweighting of small probabilities could have potentially profound implications for someone's view of insurance. A very small probability of loss may be given a much higher decision weight. That makes insurance look like a good deal. </div>
<div style="text-align: justify;">
<br /></div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-52860855296289742662017-10-10T06:16:00.002-07:002017-10-10T06:16:16.976-07:00Richard Thaler and the Nobel Prize for behavioral economics<div style="text-align: justify;">
Officially, Richard Thaler won the Nobel Prize in Economics because he 'has incorporated psychologically realistic assumptions into analyses of economic decision-making. By exploring the consequences of limited rationality, social preferences, and lack of self-control, he has shown how these human traits systematically affect individual decisions as well as market outcomes'. </div>
<div style="text-align: justify;">
<span style="background-color: white; color: #555555; font-family: "Open Sans", sans-serif; font-size: 14.4px;"><br /></span></div>
<div style="text-align: justify;">
An interesting thing about this quote is that nudge doesn't get a mention; indeed, it only just about scrapes it into the Academy's official <a href="https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2017/press.html" target="_blank">press release</a>. (In the more detailed popular information document it doesn't appear until page 5 of 6.) This is in stark contrast to the popular press: the BBC leads with 'Nudge' economist wins Nobel Prize, the Telegraph leads with 'Nudge' guru wins the Nobel Prize, and so on. To read the papers you would think that Nudge is all there is to it.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
There is no doubt that Nudge has been a huge success and made Thaler famous (at least by economist standards). In terms of the Nobel prize, however, it is important to recognize that Nudge is just one of the many, many contributions Thaler has made to economics, and behavioral economics. Let me pick up three of those contributions here.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
1. Thaler showed how dumb people can be when making economic decisions. The likes of Herbert Simon, Amos Tversky and Daniel Kahneman paved the way by showing that people can make decisions that are inconsistent with the standard way economists think about things. They, though, typically considered settings that are pretty complex, such as, search, choice with risk or how to interpret information. Thaler took this one stage further and showed that even for the most basic of economic decisions the standard economic model can go astray. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Consider, by way of illustration the following example, from the classic paper on '<a href="http://pubsonline.informs.org/doi/abs/10.1287/mksc.4.3.199" target="_blank">mental accounting and consumer choice</a>':</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Mr. S admires a $125 cashmere sweater at the department store. He declines to
buy it, feeling that it is too extravagant. Later that month he receives the same sweater
from his wife for a birthday present. He is very happy. Mr. and Mrs. S have only joint
bank accounts. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Standard economic theory says that the sweater is either worth $125 or not. But, there seems nothing extraordinary about Mr. S's behavior. To provide a framework within which to make sense of this, and much else, Thaler introduced the notion of mental accounting where we code gains and losses, evaluate purchases and observe budgetary rules. Mr. S would be breaking self-imposed rules to spend $125 from his 'everyday account' but an occasional gift funded from the 'gift account' is to be enjoyed. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Once we see how easily the framing of a choice can influence behavior it is a relatively short step to Nudge and the idea that framing can be used to positively change behavior. (Crucial in this is also the recognition that people can have self-control problems.) </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
2. As well as dumb, people can also be nice, and not so nice. In many ways economists have clung to the notion of selfishness for much longer than that of rationality. Work by Thaler helped turn the tide. Two papers with Daniel Kahneman and Jack Knetsch on '<a href="http://www.jstor.org/stable/1806070" target="_blank">Fairness as a constraint on profit taking</a>' and '<a href="http://www.jstor.org/stable/2352761?seq=1#page_scan_tab_contents" target="_blank">Fairness and the assumptions of economics</a>' are particularly noteworthy. In the first paper we get a series of questions like the following:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
A hardware store has been selling snow shovels for $15. The morning after a large snowstorm, the store raises the price to $20. Please rate this actions as: Completely fair, acceptable, unfair, very unfair.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
82% of subjects considered it unfair. Presumably that means they may decide not to buy the snow shovel; fairness matters. In the second paper we get some big advances in the studying of the ultimatum game (first use of strategy method to look at willingness to reject and first look at willingness of a third party to punish) and we see the dictator game for the first time. This may sound a bit technical but it was part of opening up the whole debate on how fairness works and can be modeled by economists.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
3. Popularization is not the kind of thing that wins Nobel prizes, but it can be important in driving things forward. In a series of articles published in the Journal of Economic Perspectives (and subsequently turned into the book <i>The Winner's Curse</i>) Thaler and co-authors set out some of the key insights of behavioral economics. I will quote in full the introduction to one of the <a href="http://www.jstor.org/stable/1942711?seq=1#page_scan_tab_contents" target="_blank">articles</a>:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Economics can be distinguished from other social sciences by the belief that
most (all?) behavior can be explained by assuming that agents have stable,
well-defined preferences and make rational choices consistent with those preferences
in markets that (eventually) clear. An empirical result qualifies as an
anomaly if it is difficult to "rationalize," or if implausible assumptions are
necessary to explain it within the paradigm. This column presents a series of
such anomalies. Readers are invited to suggest topics for future columns by
sending a note with some reference to (or better yet copies of) the relevant
research. Comments on anomalies printed here are also welcome. After this issue, the "Anomalies" column will no longer appear in every
issue and instead will appear occasionally, when a pressing anomaly crosses
Dick Thaler's desk. However, suggestions for new columns and comments on
old ones are still welcome. Thaler would like to quash one rumor before it gets
started, namely that he is cutting back because he has run out of anomalies. Au
contraire, it is the dilemma of choosing which juicy anomaly to discuss that takes
so much time.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The interesting thing about this is the target audience. This is about trying to convince economists that behavioral economics matters and should be taken seriously. That is a very hard sell indeed! But ultimately it seems to have worked.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
With any Nobel prize there are going to be the critics. And I can already hear some grumbles. But, that seems to come more from ignorance than judgement. If we take Nudge out of the equation the contributions of Thaler are clear enough. With Nudge there is undeniably a lot of hyperbole from some policy makers and consultants. The undeniable truth, however, is that it has made a positive difference to policy making. That is worth celebrating. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-90807599450851924102017-09-07T00:41:00.001-07:002017-09-07T00:41:44.231-07:00Honesty around the worldIn my last post I looked at dishonesty in the banking industry. Sticking with a similar theme, this time I will at dishonesty across different countries.<br />
<div style="text-align: justify;">
Let us start with a <a href="http://www.sciencedirect.com/science/article/pii/S0167268115001304" target="_blank">study</a> by David Pascual-Ezama and a long list of co-authors on 'Context dependent cheating: Experimental evidence from 16 countries'. They asked 90 students in 16 different countries to perform a very simple task: toss a black and white coin and record the outcome. If the coin came up white the student obtained a red Lindt Lindor Truffle. If it came up black they got nothing. Crucially, the coin toss took place in private and so the student could report whatever outcome they wanted. If they wanted a chocolate then they simply had to report white. (The study contrasted three different methods of reporting - form put in a box, form given to the experimenter or verbally telling the experimenter - but I will skip those details here.)</div>
<div style="text-align: justify;">
The chart below summarizes the country wide outcomes by focusing on the proportion of the 90 students in each country that 'won' the chocolate. The blue bars give the distribution we would predict if the students reported honestly. As you would expect the distribution is centered on a 50-50 success rate. Compared to this benchmark students were remarkably lucky. In all countries more than 50% of students won the chocolate and in some, such as Spain, the success rate was much higher than seems plausible. So, some students were dishonest (and hungry). Note, however, that the success rates are nowhere near the 100% we would expect if all students lied. So, many students were honest (or not so hungry). Indeed, we could conclude that <i>most students were honest</i>. There is also no compelling evidence of differences across countries. Spaniards won more than Danes but then someone has to come top and someone bottom. The differences we see here are not particularly large. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0iyyPEtDdg_dXkQzFMC35anvGX4tPjxmwkxULoLpTj8E9-DRuRpteMAe26szXS1GjZ5B7JhT3FBMlfyLNBLWdJClq1nycXpIYu2DAmNz1kT5zObf7FOFjJKYo3uRnOqGc9WGTTprLgZ4/s1600/Honesty.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="288" data-original-width="480" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0iyyPEtDdg_dXkQzFMC35anvGX4tPjxmwkxULoLpTj8E9-DRuRpteMAe26szXS1GjZ5B7JhT3FBMlfyLNBLWdJClq1nycXpIYu2DAmNz1kT5zObf7FOFjJKYo3uRnOqGc9WGTTprLgZ4/s640/Honesty.jpg" width="640" /></a></div>
<div style="text-align: justify;">
<br />
Consider next a <a href="http://www.sciencedirect.com/science/article/pii/S016726811630052X" target="_blank">study</a> by David Hugh-Jones on 'Honesty, beliefs about honesty, and economic growth in 15 countries'. In this case the subject pool in each country was a sample of the general population selected by a survey company and the prize was either $3 or $5 and not a chocolate. (The study also involved other measures of dishonesty and beliefs about dishonesty but I'll skip those here.) The findings are summarized in the next figure. The main thing to note is that we get a big swing to the right in those who 'won'. In other words there was a lot more dishonesty in this study. Moreover, the amount of dishonesty significantly varied across countries. Just how much we can read into this variation is not clear. For instance, the US and Canada come out as relatively dishonesty but that may reflect a willingness to 'game' the experiment rather than a predisposition to dishonesty in general life. Even so, it is shown that honesty correlates with GDP per capita and the proportion of the population that is protestant. This hints at cultural roots of honesty.<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgriClYE7QQIHMTbaxgYG6WI9GbXfhTjQtgKSyEmTVQ95kY1J84PZHmfl4L_rOE-cpw-tp5DFTY8bjwgvbNSH3JmbONFfezkrotKbZ2yFwRkeD-X80jLbDcy1zXr5G889oMoouA8yRrZ0M/s1600/Honesty2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="288" data-original-width="441" height="416" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgriClYE7QQIHMTbaxgYG6WI9GbXfhTjQtgKSyEmTVQ95kY1J84PZHmfl4L_rOE-cpw-tp5DFTY8bjwgvbNSH3JmbONFfezkrotKbZ2yFwRkeD-X80jLbDcy1zXr5G889oMoouA8yRrZ0M/s640/Honesty2.jpg" width="640" /></a></div>
<br />
Which brings us to the final <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4817241/" target="_blank">study</a> I will mention, by Simon Gachter and Jonathon Schultz on 'Intrinsic honesty and the prevalence of rule violations across countries'. In this study students from 23 countries were asked to roll a six sided dice and report the outcome. Reporting a 1 earned 1 unit of payment (e.g. £0.50 in the UK), a 2 earned 2 units and so on up to 5 which earned 5 units, but reporting a 6 earned 0. Note that in this experiment a subject can lie 'a little' by say reporting 4 instead of 2 or lie 'a lot' by reporting 5 instead of 6. If subjects were honest the expected payment would be 2.5. If they lied a lot the payment would be 5. As the figure below shows average payments were well above 2.5 and so there is evidence of dishonesty. Note, however, that payments were well below 5 and so there is, again, lots of honesty as well.<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhICZYH2yTI4_0nfkjvjtEgIzzqt-SyRk1u2h2E327E-YZkf8gcIOROuYKRzA_vkdFi5H6A7k7b_JfEYoTa3ati7a_akuvCw1kK5_8b5LuZUVMzrnTUb126UlkE9LPg5-yRnznYtgMPLzQ/s1600/Honesty3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="288" data-original-width="534" height="344" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhICZYH2yTI4_0nfkjvjtEgIzzqt-SyRk1u2h2E327E-YZkf8gcIOROuYKRzA_vkdFi5H6A7k7b_JfEYoTa3ati7a_akuvCw1kK5_8b5LuZUVMzrnTUb126UlkE9LPg5-yRnznYtgMPLzQ/s640/Honesty3.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
<br />
Cross country differences are not partly stark in the figure above. But another thing to consider is the proportion of subjects who reported a 6. Recall that this meant a payoff of 0 and so there was a strong incentive to lie 'a little' and get some payoff. (Indeed, to not report a 6 would seem analogous to miss-reporting the toss of a coin.) If subjects were honest around 16% should get 0. As the figure below shows in some countries, like Germany, subjects were very honest but in others, like Tanzania, they were not. And evidence for differences across countries is pretty strong. Overall, it is shown that cross country differences correlate strongly with an index of the prevalence of rule violations which captures things like corruption, tax evasion and fraudulent politics. This again points the finger at culture but also brings in the related issue of institutions. Countries with weak institutions see more dishonesty.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJUaEl0JoG5iMhmddJ5sq1anqWDU-nwtt-EpED0PGp7_-nKcmJoQTOD1oeDahjS8-N67ZC3XWQIHPd-kIcSpIqXVOK2LCJqm6m_vk4DGlB5nGt086L82QyjkAYf5M6fCMiOEi-7KVSHX0/s1600/Honesty4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="288" data-original-width="534" height="344" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJUaEl0JoG5iMhmddJ5sq1anqWDU-nwtt-EpED0PGp7_-nKcmJoQTOD1oeDahjS8-N67ZC3XWQIHPd-kIcSpIqXVOK2LCJqm6m_vk4DGlB5nGt086L82QyjkAYf5M6fCMiOEi-7KVSHX0/s640/Honesty4.jpg" width="640" /></a></div>
<br />
So, what to take from all this? One message I would take is that people are, on average, very honest. In all the three studies I have discussed there was more subjects behaved honestly than dishonestly. And let's recall that it was pretty easy for a subject to lie in these studies, both in a practical sense - they just needed to misreport - and in a moral sense - this was not robbing money from an old lady. It seems, therefore, that people the world over are pretty honest. But, that does not mean that dishonesty is not a problem. In my last post we saw that culture in the banking industry might encourage dishonesty. Here we see that culture in society might lead to greater dishonesty. A little bit of dishonesty can have large negative economic consequences. <br />
<br /></div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-54747992447187482582017-08-27T01:00:00.001-07:002017-08-27T01:00:42.278-07:00Culture and dishonesty in banking<div style="text-align: justify;">
The film 'A Good Year' starts with a ruthless financial trader called Max, played by Russell Crowe, manipulating bond markets in order to out-maneuver his competitors and make a quick, big profit. But, by the end of the film Max has decided to pack it all in and live out a more fulfilling life in rural France. Could that happen? Can someone really transition from a ruthless, selfish trader to a compassionate, loving family man in the space of a few days?</div>
<div style="text-align: justify;">
A <a href="http://www.nature.com/nature/journal/v516/n7529/full/nature13977.html?foxtrotcallback=true" target="_blank">study</a> by Alain Cohn, Ernst Fehr and Michel Marechal, publisehd in 2014 in Nature, suggests it might be possible. They used a standard coin tossing task to measure the dishonesty of 128 employees from a large, international bank. The task works as follows: A subject is asked to toss a coin 10 times and record whether the outcome was heads or tails. Depending on the outcome the subject can win $20 per toss. The crucial thing to know is that the subject records whether or not they won for each toss and there is no way for the experimenter to verify if the outcome is recorded correctly. So, the subject fills in the following table privately. This means a subject could 'easily' lie and walk away with $200.</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2OK0ny73s3fr6xq20lUeJT_zrDdbcML6YIwJ8UUmmoSnvYdD_KZfkrdf-RXGZ0sVXoqQ4trka2nJ7VMnk0MfgjRahgm8vXDKaD5rSDCT2wvTcEuHUq4ZAohWltRhFaDIGXOpfi8IBR3A/s1600/CoinToss.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="561" data-original-width="617" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2OK0ny73s3fr6xq20lUeJT_zrDdbcML6YIwJ8UUmmoSnvYdD_KZfkrdf-RXGZ0sVXoqQ4trka2nJ7VMnk0MfgjRahgm8vXDKaD5rSDCT2wvTcEuHUq4ZAohWltRhFaDIGXOpfi8IBR3A/s320/CoinToss.jpg" width="320" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The crucial twist in the experiment was to vary the priming subjects faced before performing the coin-tossing task. Roughly half of the subjects were asked questions related to their work in the bank - Why did you decide to become a bank employee? What are the three major advantages of your occupation as a bank employee? Which three characteristics of your personality do you think are typical for a bank employee? etc. The other half of the subjects were asked questions not related to their work - What is your favorite leisure activity? Where did you spend your last vacation? Which three things did you like most about your last vacation? etc. </div>
<div style="text-align: justify;">
So, to the results. The figure below shows what happens for subjects <b>not</b> primed to think about work in the bank. The blue bars show the observed distribution of earnings and the green bars show the distribution of earnings expected by pure chance. We can see some hints of dishonesty - there are fewer than we would expect getting $40 or less and more getting $200. But, these are small things. The overall picture is that the <i>bankers were honest.</i> </div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLbER1SseNNz6zAsEVdvTimkz0PU734u889eyLVIjZKBTGtp0EjobtAuREKNbwaTOavnta7WnM6Lzl1jUDOWp5oB0_uBi0xbZStn3Mly7VkM_2EA8hHA_SzEf2L449szszMsmNCGW8Ems/s1600/CoinTossNoPrime.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="259" data-original-width="408" height="253" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLbER1SseNNz6zAsEVdvTimkz0PU734u889eyLVIjZKBTGtp0EjobtAuREKNbwaTOavnta7WnM6Lzl1jUDOWp5oB0_uBi0xbZStn3Mly7VkM_2EA8hHA_SzEf2L449szszMsmNCGW8Ems/s400/CoinTossNoPrime.jpg" width="400" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Things change when subjects were primed to think about work in the bank. The distributions are shown below. Here we see a sizable increase in the amount of money being claimed. Needless to say, this is highly unlikely to be due to chance. It can be estimated that around 26% of subjects were dishonesty. Let us keep in perspective that this means 74% were honest. Even so, the headline result is that <i>bankers only exhibit dishonesty when they are primed to think about banking</i>.</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLB_sV3xgzBqvNmH3UPThW12jpLc2gxKOc3YMRAeL2mt1e63lxKPq1B8qJJ-o7wPIm4Va9IXM98rbzzTw6XzgbCDt9HmnnEZBHtIbaaEJxhClxIgx7uZ2IDkMbHXPzOfVWlZJ-RYK-K0c/s1600/CoinTossPrime.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="259" data-original-width="408" height="253" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLB_sV3xgzBqvNmH3UPThW12jpLc2gxKOc3YMRAeL2mt1e63lxKPq1B8qJJ-o7wPIm4Va9IXM98rbzzTw6XzgbCDt9HmnnEZBHtIbaaEJxhClxIgx7uZ2IDkMbHXPzOfVWlZJ-RYK-K0c/s400/CoinTossPrime.jpg" width="400" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
This finding feeds into a general debate about whether dishonesty is a personal trait or a product of culture. The results we have looked at here suggest that dishonesty has a large cultural component. That would make it more likely a banker can be ruthless in his job and then help old ladies across the road in his spare time. It is hard to imagine, however, that culture is the only factor at work here because we do know that there are reliable personal differences in dishonesty and willingness to cooperate. It is surely not by chance that some become investment bankers and others pediatricians? An interesting and closely related debate is whether studying economics makes people more selfish (culture at play) or whether more selfish people choose to study economics (personal traits at play). An <a href="http://evonomics.com/more-evidence-that-learning-economics-makes-you-selfish/" target="_blank">article by Adam Grant</a> provides a nice overview of the issues. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-6070999982641579922017-07-28T23:21:00.001-07:002017-07-28T23:21:21.532-07:00Risk aversion or loss aversion<div style="text-align: justify;">
Suppose you offer someone called Albert a gamble - if the toss of a coin comes up heads then you pay him £100 and if it comes up tails he pays you £100. The evidence suggests that most people will not take on that gamble. If Albert also turns down the gamble, what does that tell you about Albert's preferences?</div>
<div style="text-align: justify;">
One thing we can conclude is that Albert is risk averse. In particular, the gamble was fair because Albert's expected payoff was 0 and, by definition, if someone turns down a fair gamble then they are exhibiting risk aversion. It is hard to argue with a definition and so we can conclude that Albert is risk averse. The more interesting question is why he displays risk aversion?</div>
<div style="text-align: justify;">
The micro-economic textbook would tell us that it is because of diminishing marginal utility from money. A diagram helps explain the logic. Suppose that Albert has the utility function for money depicted below. In this specific case I have set the utility of £m as the square root of m. Notice that the utility function is concave in the sense that it gets flatter for larger amounts of money. This is diminishing marginal utility of money - the more money Albert has the less he values more. </div>
<div style="text-align: justify;">
Suppose that Albert has £500. If he does not take the gamble then his utility is 22.36. If he takes the gamble then he can end up with either £400 or £600. The former gives him utility 20 and the latter 24.49. The expected utility is midway between this, i.e. 22.25. Crucially the expected utility of the gamble, 22.25, is less than not taking on the gamble, 22.36, and so Albert does not gamble. As the bottom figure shows we get this result because the utility function is concave. That means the utility of not gambling - on the blue line - lies above the expected utility of gambling - on the red line. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibtG2OiNvoLYy1ij6ZgYpkw6kDbIMZOmDY54o-hC5R-Bq1HEe2SLtS1w9PZR5sivzclLHUaC9-cO0ZO48gpGn-KVfXMCHEqP6p0vACQ2rx6tgEA3zBPXgThKnJzlN4hMmXLgd-PGr_UHw/s1600/riskAverse.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="546" data-original-width="475" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibtG2OiNvoLYy1ij6ZgYpkw6kDbIMZOmDY54o-hC5R-Bq1HEe2SLtS1w9PZR5sivzclLHUaC9-cO0ZO48gpGn-KVfXMCHEqP6p0vACQ2rx6tgEA3zBPXgThKnJzlN4hMmXLgd-PGr_UHw/s1600/riskAverse.jpg" /></a></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
There is though a problem with this standard story, formally demonstrated by Matthew Rabin in a 2000, <i>Econometrica</i> paper '<a href="http://onlinelibrary.wiley.com/doi/10.1111/1468-0262.00158/full" target="_blank">Risk aversion and expected utility theory: A calibration theory</a>'. If Albert is risk averse over a relatively small sum of money like 100 with an initial wealth of £500 then he would have to be unbelievable risk averse over large gambles. Basically, he would never leave his front door. If diminishing marginal utility of money is not the explanation for Albert's risk aversion then what is?</div>
<div style="text-align: justify;">
The most likely culprit is loss aversion. Now we have to evaluate outcomes relative to a reference point rather than a utility function over wealth. It seems natural to think that Albert's reference point is £500. That would mean winning the gamble is a gain of £100 and losing the gamble is a loss of £100. Crucially, the evidence suggests that people typically interpret a loss as worse than a gain is good. This is shown in the next figure. <br />
In this case everything is judged relative to the status quo of £500. Having more than £500 is a gain and less than £500 is a loss. The steeper value function below £500 captures loss aversion. The crucial thing to observe is that loss aversion effortlessly gives concavity of the value function around the status quo. So, Albert would prefer to not gamble and have value 0 than to gamble and have either +5 or -10 with an expected value of -2.5. Loss aversion has no problem explaining risk aversion over small gambles. <br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju8cNDzzukJPmV258-BzQFAFcuUz6oGyzWvKIwlGYWOAhWHXZ0xcIaC6VKrMO8l_aohGoEsv_Yf2NCVvepzndHMdt7wajnTvedp5VwdcdVzyBb7Q3Tz1yIxcQvs6pdwqWV5_JwiRzuiMM/s1600/lossAverse.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="551" data-original-width="479" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju8cNDzzukJPmV258-BzQFAFcuUz6oGyzWvKIwlGYWOAhWHXZ0xcIaC6VKrMO8l_aohGoEsv_Yf2NCVvepzndHMdt7wajnTvedp5VwdcdVzyBb7Q3Tz1yIxcQvs6pdwqWV5_JwiRzuiMM/s400/lossAverse.jpg" width="346" /></a></div>
<br />
<br />
So, what can we conclude from all this? The first thing to tie down is the definition of risk aversion. Standard textbooks will tell you that risk aversion is turning down a fair gamble. That to me seems like a fine definition. So far, so good. Confusion (including in academic circles) can then come from interpreting what that tells us. Generations of economists have been educated to think that risk aversion means diminishing marginal utility of money. It need not. We have seen that loss aversion can also cause risk aversion. And there are other things, like weighting of probabilities that can also cause risk aversion. It is important, therefore, to consider different possible causes of risk aversion.<br />
And it is also important to recognize that there is unlikely to be some unified explanation for all risk aversion. We know that people do have diminishing marginal utility of money over big sums of money. We know people are loss averse over surprising small amounts of money. We also know that people are bad at dealing with probabilities. All of these factors should be put in the mix. So, Albert might buy house insurance because of diminishing marginal utility of money, not try the new cafe for lunch because he is loss averse, and buy a lottery ticket because he overweights small probabilities. </div>
<div style="text-align: justify;">
<br /></div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-33470447541435268202017-05-09T06:56:00.000-07:002017-05-09T06:56:00.050-07:00Will a vote for Theresa May strengthen her bargaining hand?<div style="text-align: justify;">
As the run-up to the UK's snap general election continues, the Conservative party appear content to talk about one thing and one thing only - strong and stable leadership for Brexit negotiations. Throughout the campaign Theresa May has been particularly keen to claim that 'every vote for me strengthens my hand in the Brexit negotiations'. This claim seems to be going down well with voters. But does it make any sense?</div>
<div style="text-align: justify;">
In bargaining theory the <i>disagreement point</i> is of critical importance. In the Brexit negotiations we can think of the disagreement point as the outcome if no deal is done between the UK and the EU and so the UK simply leaves the EU in March 2019 and starts from scratch. Most experts seem to agree that no deal would be bad - very bad for the UK and bad for the EU. That means that a deal is essential. It also means that the UK starts from a bad negotiating position. </div>
<div style="text-align: justify;">
To put some analysis to this consider the figure below. This plots the payoff of the EU and payoff of the UK depending on what deal is done. The blue line captures all the possible outcomes from a deal - some deals better for the UK and some for the EU. The bottom red dot captures the outcome if no deal is done. Note that if no deal is done then payoffs are well below the blue line - an agreement is good. Also, if no deal is done then the UK loses more than the EU - this puts the UK in a bad negotiating position. </div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAbljziT8rQHCyF20DUP5F08sF4UsXj2hixw4vIklFLhi5OqTqBFzbz5qz7bCQmpTd3X9aNxyFHAWQpILb5oEeiBmJguv2Jbf4VadbDZxb5PbylvYb9BqLwMAjzFh2iwKFEdX9vw9_dsQ/s1600/Brexit.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAbljziT8rQHCyF20DUP5F08sF4UsXj2hixw4vIklFLhi5OqTqBFzbz5qz7bCQmpTd3X9aNxyFHAWQpILb5oEeiBmJguv2Jbf4VadbDZxb5PbylvYb9BqLwMAjzFh2iwKFEdX9vw9_dsQ/s640/Brexit.jpg" width="640" /></a></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
In a world of calm deliberation the EU and UK could easily come to an agreement that is better than no deal. But, unfortunately, some Brexiters seem to have got over excited by the referendum win and started to believe their own rhetoric. In particular, they are claiming that no deal is not that bad. This is encapsulated by Theresa May's claim that 'no deal is better than a bad deal'. This statement is either a tautology or a claim that no deal may be relatively good. Brexiters are also fond of claiming that no deal would be worse for the EU than the UK. So, returning to the figure, let the red Eurosceptic dot represent the 'optimistic' stance of Brexiters.<br />
Before she called an election, Theresa May had a small majority in parliament. That means it was going to be difficult to get anything through parliament that the eurosceptics did not like. And there is not much room for maneuver if you want do a deal better than the eurosceptic initial belief. Note, however, that this <i>strengthened</i> Theresa May's hand quite a lot. In particular, European politicians seemed keenly aware that it was going to be difficult to get any deal through the UK parliament. This means that they might have reluctantly had to make some concessions.<br />
What if Mrs May has a huge majority in parliament? Well, then anything will get through parliament and so we revert back to the actual disagreement point. The bigger the majority, therefore, the <i>weaker</i> is the UK's position. Ultimately, things are not so bad, because a Conservative majority makes it more likely a deal can be done. Indeed, Theresa May presumably called an election because it was becoming increasingly clear that Conservative backbenchers were going to make life very tough. This made no deal more likely.<br />
The trouble is, the rhetoric of the Brexiters seems to have no bound. This rhetoric is not convincing anyone in Europe but is being lapped up by much of the British press and public. If we go into these negotiations with a public who think the initial position is the top eurosceptic red dot then it may be difficult for any prime-minister, no matter how big the majority, to sell a deal. In other words, Britain seems to be walking into a cul-de-sac of disaster. The only crumb of comfort is that the UK economy seems to be showing the signs of Brexit. That may concentrate minds. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-5815094182712944782017-03-28T08:08:00.003-07:002017-03-28T08:08:51.420-07:00Brexit and the Condorcet Paradox<div style="text-align: justify;">
Tomorrow the government will trigger Article 50 and start the formal process of getting the UK out of the EU. So, how did we get in this mess in the first place? I think the Condorcet Paradox provides an interesting angle on the problem. In particular, I want to look at preferences for Remain versus Soft Brexit, i.e. leave the EU but still remain in the single market or other collaborations centered on the EU, and Hard Brexit, i.e. walk completely away from the EU. </div>
<div style="text-align: justify;">
The one thing we know for sure is that in the referendum last June around 52% of people voted Leave and 48% voted Remain. What does that tell us? In my recollection the referendum campaign primarily focused on the question of Soft Brexit versus Remain. No doubt some would disagree with that. But things like the customs union only started being talked about after the vote. Instead we heard a lot during the campaign about the Norway or Swiss model of Soft Brexit. True the Leave camp made promises like 'take back control of our borders' that inevitably mean hard Brexit. But, the Leave camp was far less pro-active in actually joining the dots and saying what hard Brexit would mean. The referendum vote tells us, therefore, that the British people <i>prefer Soft Brexit to Remain</i>.</div>
<div style="text-align: justify;">
Once Theresa May took power the discussion very quickly turned to focus on Soft Brexit versus Hard Brexit. Now, the Brexiters were keen to join the dots and argue that 'taking back control' inevitably meant Hard Brexit. Soft Brexit, they argue, is essentially Remain in different clothes - if we are going to leave then it has to be Hard Brexit. We have no idea how the country would vote on this issue but I think there is a fair chance the country would <i>prefer Hard Brexit to Soft Brexit</i>. </div>
<div style="text-align: justify;">
If the country prefers Hard Brexit to Soft Brexit and prefers Soft Brexit to Remain then you might expect they would prefer Hard Brexit to Remain. But, I would be surprised if that was the case. If the original referendum campaign had been a tussle between Hard Brexit and Remain then Remain may well have won. The vote was close enough as it was and opinion polls have consistently shown that people want to remain part of the single market. Overall, therefore, we end up with a Condorcet Paradox:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Hard Brexit beats Soft Brexit</div>
<div style="text-align: justify;">
Soft Brexit beats Remain</div>
<div style="text-align: justify;">
Remain beats Hard Brexit.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
If there is a Condorcet Paradox then it is impossible to say which option is the most preferred. Note, however, that we are set to end up with an outcome, namely Hard Brexit, that is worse than we started with, namely Remain. That does not look like a good deal! Plaudits should, however, go to the Brexiteers for their strategic opportunism. In particular, we know that whenever there is a Condorcet Paradox the outcome depends on the voting procedures. The only way those favoring Hard Brexit were going to get what they wanted was to play off Soft Brexit versus Remain and Hard Brexit versus Soft Brexit. By design or good fortune that is exactly what has happened. </div>
<div style="text-align: justify;">
And are we going to get a vote on the final deal, pitting Remain versus Hard Brexit? Of course not. And how long before the UK votes to rejoin the EU because Join is better than Hard Brexit? Probably, a long, long while. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-44467305444694507232017-03-20T06:52:00.001-07:002017-03-20T06:52:15.896-07:00How to get rid of an incompetent manager?<div style="text-align: justify;">
In a <a href="https://link.springer.com/article/10.1007/s00182-017-0570-1" target="_blank">paper</a>, recently published in the <i>International Journal of Game Theory</i>, my wife and I analyze a game called a forced contribution threshold public good game. A nice way to illustrate the game is to look at the difficulties of getting rid of an incompetent manager.<br />
So, consider a department with n workers who all want to get rid of the manager. If they don't get rid of him then there payoff will be L. If they do get rid of him then there payoff will be H > L. But, how to get rid of him? He will only be removed if at least t or more of the workers complain to senior management. For instance, if a majority of staff need to complain then t = n/2.<br />
If t or more complain then the manager is removed and everyone is happy. The crucial thing, though, is what happens if less than t complain. In this case the manager will remain and any workers that did complain will face recrimination. To be specific suppose that the cost of recrimination is C. Then potential payoffs to a worker called Jack are as follows:<br />
<br />
If t or more complain then Jack gets payoff H.<br />
If Jack complains but not enough others do then he gets payoff L - C.<br />
If Jack does not complain and others don't either then he gets payoff L.<br />
<br />
Note that this game is called a 'forced' contribution game because, if the manager is removed, Jack's payoff does not depend on whether or not he complained. This contrasts with a standard threshold public good game in which those who do not contribute (i.e. complain) always have a relative advantage. Hence, there is a sense in which every worker is 'forced to contribute' if the manager is removed.<br />
The fear of recrimination is key to the game and going to be the potential source of inefficiency. In particular, if Jack fears that others will not complain then it is not in his interest to complain either. Hence we can obtain an inefficient equilibrium in which nobody complains and the manager carries on before. This is not good for the workers and presumably not good for the firm either. So, how can this outcome be avoided?<br />
In our paper we compare the predictions of three theoretical models and then report an experiment designed to test the respective predictions. Our results suggest that the workers will struggle to get rid of the manager if<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaPuspVEN4MpeZaJEIHfzHvRZQoFTNAh7GTXhcbf0rfjWp3jwvfIAMdy5hUMo_Pm3UKBR3pd4FWPIhH0h82VAFXc_EtL8Wr1U0VTGO6mPTKo3YSUiWrCNCwiJJY99WHW3asGj_npGF7UE/s1600/FC.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaPuspVEN4MpeZaJEIHfzHvRZQoFTNAh7GTXhcbf0rfjWp3jwvfIAMdy5hUMo_Pm3UKBR3pd4FWPIhH0h82VAFXc_EtL8Wr1U0VTGO6mPTKo3YSUiWrCNCwiJJY99WHW3asGj_npGF7UE/s1600/FC.png" /></a></div>
This means that the threshold t should not be set too high. For instance, if a simple majority is needed to get rid of the manager, and so t = n/2, then we need H to about 25% higher than L. If less than a majority is enough then H does not need to be as high. This result would suggest that it is relatively simple to have a corporate policy that would incentivise people like Jack to complain about his manager.<br />
Of course, in practice there are almost certainly going to be some who will defend the manager and so things become more complex. Moreover, there are likely to be significant inertia effects. In particular, the 'better the devil you know' attitude may lead workers to underestimate the difference between H and L. Also senior managers may set t relatively high because of a desire to back managers. These are all things that will make it less likely Jack complains and more likely the incompetent manager continues. Firms, therefore, need to strike the right balance to weed out inefficiency. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-46905291341537948752017-02-25T08:21:00.000-08:002017-02-25T08:21:07.523-08:00Measuring risk aversion the Holt and Laury way<div style="text-align: justify;">
Attitudes to risk are a key ingredient in most economic decision making. It is vital, therefore, that we have some understanding of the distribution of risk preferences in the population. And ideally we need a simple way of eliciting risk preferences that can be used in the lab or field. Charles Holt and Susan Laury set out one way of doing in this in their 2002 paper '<a href="https://www.aeaweb.org/articles?id=10.1257/000282802762024700" target="_blank">Risk aversion and incentive effects</a>'. While plenty of other ways of measuring risk aversion have been devised over the years I think it is safe to say that the Holt and Laury approach is the most commonly used (as the near 4000 citations to their paper testifies). </div>
<div style="text-align: justify;">
The basic approach taken by Holt and Laury is to offer an individual 10 choices like those in the table below. For each of the 10 choices the individual has to go for option A or option B. Most people go for option A in choice 1. And everyone should go for option B in choice 10. At some point, therefore, we expect the individual to switch from choosing option A to option B. The point at which they switch can be used as a measure of risk aversion. Someone who switches early is risk loving while someone who switches later is risk averse.</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjmHgkbn88ALfoZa1sOzQ72oExPyHvntCyncTOfhbDfsGg73ZmmJ8eRtptRtkkvs8WIDWoDzQE1cH_015i6Pne5ybKzxl8JV9o6y_mXUU1jbjFJIPRyxVl7UPpTV7VGFzgbAjevPKO1q4/s1600/HL.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjmHgkbn88ALfoZa1sOzQ72oExPyHvntCyncTOfhbDfsGg73ZmmJ8eRtptRtkkvs8WIDWoDzQE1cH_015i6Pne5ybKzxl8JV9o6y_mXUU1jbjFJIPRyxVl7UPpTV7VGFzgbAjevPKO1q4/s640/HL.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
To properly measure risk aversion we do, though, need to fit choices to a utility function. This is where things get a little tricky. In the simplest case we would be able to express preferences using a constant relative risk aversion (CRRA) utility function </div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVSrrNjQTs_iU89ZA5n9Xj3IGd2257m8j8awhWJEMulEDJyXvU1fPbeazVDvqyXi7xOdQpEUSx_W57kujEVVexQTgrkOc0xyDcQCaNg5MSTw20k97pYXJHiOFbKPEpHtI35FWd2AQzrA4/s1600/CRRA.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVSrrNjQTs_iU89ZA5n9Xj3IGd2257m8j8awhWJEMulEDJyXvU1fPbeazVDvqyXi7xOdQpEUSx_W57kujEVVexQTgrkOc0xyDcQCaNg5MSTw20k97pYXJHiOFbKPEpHtI35FWd2AQzrA4/s1600/CRRA.jpg" /></a></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
where x is money. I can come back to why this is the simplest case shortly. First, let's have a quick look how it works. Suppose that someone chooses option A for choice 4. Then we can infer that</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNZzt4npgOCK1UdmuZajK2fyBhVWaoOtBRVvsvOapnzzhPcsdvFL3jQDMvRD2J39-CPpCbyehwAdcAwwqCN8Z1qxjVSqPJPJ7AZMcgI06w0DG2CygG19te_FF_M1UQNkjCL6KmGmmtAM4/s1600/choice4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNZzt4npgOCK1UdmuZajK2fyBhVWaoOtBRVvsvOapnzzhPcsdvFL3jQDMvRD2J39-CPpCbyehwAdcAwwqCN8Z1qxjVSqPJPJ7AZMcgI06w0DG2CygG19te_FF_M1UQNkjCL6KmGmmtAM4/s1600/choice4.jpg" /></a></div>
<div style="text-align: justify;">
It is then a case of finding for what values of r this inequality holds. And it does for r less than or equal to around -0.15. Suppose the person chooses option B for choice 5. Then we know that</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgfxp3uLX3lm_7j9o48YzcRqT0eXKWun10XuUnubi2r7BehJxDYXHU9wDy2ws27-RJCLqt-cBEogqJkNdUMBZ-IL-QCbHrDRzAQsNKCj6sZr67tk91FlanQwirl_q0M26r2beLVGuRMaY/s1600/choice5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgfxp3uLX3lm_7j9o48YzcRqT0eXKWun10XuUnubi2r7BehJxDYXHU9wDy2ws27-RJCLqt-cBEogqJkNdUMBZ-IL-QCbHrDRzAQsNKCj6sZr67tk91FlanQwirl_q0M26r2beLVGuRMaY/s1600/choice5.jpg" /></a></div>
<div style="text-align: justify;">
This time we get r grater than or equal to around 0.15. So, A person who switches between questions 4 and 5 has a relative risk aversion of between -0.15 and 0.15.</div>
<div style="text-align: justify;">
Let us return now to the claim that a CRRA function keeps things simple. The dollar amounts in the choices above are small. What happens if we make them bigger? Holt and Laury tried multiplying them by 20, 50 and 90. Note that by the time we get to multiplying by 90 the amounts are up to $180 which is quite a lot of money for an experiment. If the CRRA utility function accurately describes preferences then people should behave exactly the same no matter how big the stakes. This would be ideal. Holt and Laury found, however, that people were far more likely to choose option A when the stakes were larger. Which means the CRRA function did not well describe subjects choices. </div>
<div style="text-align: justify;">
So, what does the rejection of CRRA mean? It tells us that just asking someone to make the 10 choices above is not enough to discern their preferences for risk. We learn what they would do for those magnitudes of money but cannot extrapolate from that to larger amounts. We cannot, for instance, say that someone is risk averse or risk loving because that person might appear risk loving for gambles over small amounts of money and risk averse for larger amounts. To fully estimate risk preferences we need to elicit choices over gambles with varying magnitudes of money.</div>
<div style="text-align: justify;">
Despite all this, it is pretty standard to run the Holt and Laury approach at the end of experiments. The basic goal of doing so is to see if behavior in the experiment, say on public goods, correlates with attitudes to risk. Note that the simplicity of the Holt and Laury approach is a real draw here because you don't want to add something overly complicated to the end of an experiment. Care, though, is needed in interpreting results. As we have seen the Holt and Laury approach is not enough to parameterize preferences. All we can basically infer, therefore, is that one subject is relatively more or less risk averse or loving than another. This, though, is informative as a rough measure of how attitudes to risk influence behavior. Key, therefore, is to focus on relative rather than absolute comparisons.</div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0tag:blogger.com,1999:blog-8737560838408149895.post-28928933440684900582017-02-21T06:20:00.001-08:002017-02-21T06:20:58.990-08:00Does a picture make people more cooperative<div style="text-align: justify;">
In a standard economic experiment the anonymity of subjects is paramount. This is presumably because of a fear that subjects might behave differently if they knew others were 'watching them' in some sense. In the real world, however, our actions obviously can be observed much of the time. So, it would seem important to occasionally step out of the purified environment of the standard lab experiment and see what happens when we throw anonymity in the bin.</div>
<div style="text-align: justify;">
A couple of experiments have looked at behavior in public good games without anonymity. Let me start with the 2004 study of Mari Rege and Kjetil Telle entitled '<a href="http://the%20impact%20of%20social%20approval%20and%20framing%20on%20cooperation%20in%20public%20good%20games/" target="_blank">The impact of social approval and framing on cooperation in public good games</a>'. As is standard, subjects had to split money between a private account and group account, where contributing to the group account is good for the group. The novelty is in how this was done.<br />
Each subject was given some money and two envelopes, a 'group envelope' and 'private envelope', and asked to split the money between the envelopes. In a no-approval treatment the envelopes were then put in a box and mixed up before they were opened up and the contributions read out aloud. Note that in this case full anonymity is preserved because the envelopes are mixed up. In an approval treatment, by contrast, subjects were asked to publicly open their envelopes and write the contribution on the blackboard. Here there is zero anonymity because the contribution of each subject is very public.<br />
Average contributions to the group account were 44.8% (of the total amount) in the no-approval treatment and 72.8% in the approval treatment. So, subjects contributed a lot more when anonymity was removed.<br />
Similar results were obtained by James Andreoni and Ragan Petrie in a study entitled '<a href="http://www.sciencedirect.com/science/article/pii/S0047272703000409" target="_blank">Public goods experiments without confidentiality</a>'. Here, the novelty was to have photos of subjects together with their contributions to the group account, as in the picture below. In this case contributions increased from 26.9% in the absence of photos to 48.1% with photos. Again subjects contributed a lot more when anonymity was removed.</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpl2zrttdPmvc-IZgsjcz2IaHIk1yT4nbGlc0KvAHXkIZ2GhbyVRAfYd_JVnK7k3hRnv8JMxcTZVnssYsPjEWoIClfUqiOvI2sqJAwNiWxP6Z7GDFKm1S6TbvPLCh7TeP_TLRpC_nXgVI/s1600/photos1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="379" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpl2zrttdPmvc-IZgsjcz2IaHIk1yT4nbGlc0KvAHXkIZ2GhbyVRAfYd_JVnK7k3hRnv8JMxcTZVnssYsPjEWoIClfUqiOvI2sqJAwNiWxP6Z7GDFKm1S6TbvPLCh7TeP_TLRpC_nXgVI/s400/photos1.jpg" width="400" /></a></div>
<div style="text-align: justify;">
<br />
So, why does anonymity matter? A study by Anya Samek and Roman Sheremeta, entitled '<a href="http://link.springer.com/article/10.1007/s10683-013-9389-1" target="_blank">Recognizing contributors</a>' sheds some light on this. As well as treatments with no photos and everyone's photos they had treatments in which only the lowest and only the highest contributors had their photos displayed, as in the middle picture below.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpry__yFl30PIF3H_h-Umfpy-Ajo7GHEpgA6VaeC9b0IaMbCFUvRfKJ-RwJUwMwJXJxQHgEkhqNJk6VqEp1Ym_RSBqY1zksEKxOzQgvwLdeuacWdh6E36n0XHjDc0PAbtDukyniDCvYfI/s1600/photos.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpry__yFl30PIF3H_h-Umfpy-Ajo7GHEpgA6VaeC9b0IaMbCFUvRfKJ-RwJUwMwJXJxQHgEkhqNJk6VqEp1Ym_RSBqY1zksEKxOzQgvwLdeuacWdh6E36n0XHjDc0PAbtDukyniDCvYfI/s400/photos.png" width="298" /></a></div>
<br />
Again, photos made a big difference, increasing average contributions from 23.4% to 44.2%. Interestingly, displaying the photos of top contributors made little difference (up to 27.8%) while displaying the photos of the lowest contributors made a big difference (up to 44.9%). This would suggest that contributions increase without anonymity because subjects dislike being the lowest contributors. So, we are talking shame rather than pride.<br />
What do we learn from all this? Obviously we can learn interesting things by dropping anonymity. In particular, we have learnt that contributions to group projects may be higher when individual contributions can be identified. Indeed, in a follow paper, entitled '<a href="http://onlinelibrary.wiley.com/doi/10.1002/soej.12116/full" target="_blank">When identifying contributors is costly</a>', Samek and Sheremeta show that the mere possibility of looking up photos increases contributions. That, though, raises some tough questions. If behavior is radically different without anonymity then is it good enough to keep on churning out results based on lab experiments with complete anonymity? I don't think it is. The three studies mentioned above have shown how anonymity can be dropped without compromising scientific rigor. More of that might be good. </div>
Edward Cartwrighthttp://www.blogger.com/profile/02915630637868391510noreply@blogger.com0